René's URL Explorer Experiment

Title: Triangular number - Wikipedia

Open Graph Title: Triangular number - Wikipedia

Generator: MediaWiki 1.46.0-wmf.15

Hey, it has json ld scripts:

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referrer	origin-when-cross-origin
format-detection	telephone=no
og:image	https://upload.wikimedia.org/wikipedia/commons/thumb/1/1c/First_six_triangular_numbers.svg/1280px-First_six_triangular_numbers.svg.png
og:image:width	1200
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Links:

Jump to content	https://en.wikipedia.org/wiki/Triangular_number#bodyContent
Main page	https://en.wikipedia.org/wiki/Main_Page
Contents	https://en.wikipedia.org/wiki/Wikipedia:Contents
Current events	https://en.wikipedia.org/wiki/Portal:Current_events
Random article	https://en.wikipedia.org/wiki/Special:Random
About Wikipedia	https://en.wikipedia.org/wiki/Wikipedia:About
Contact us	https://en.wikipedia.org/wiki/Wikipedia:Contact_us
Help	https://en.wikipedia.org/wiki/Help:Contents
Learn to edit	https://en.wikipedia.org/wiki/Help:Introduction
Community portal	https://en.wikipedia.org/wiki/Wikipedia:Community_portal
Recent changes	https://en.wikipedia.org/wiki/Special:RecentChanges
Upload file	https://en.wikipedia.org/wiki/Wikipedia:File_upload_wizard
Special pages	https://en.wikipedia.org/wiki/Special:SpecialPages
	https://en.wikipedia.org/wiki/Main_Page
Search	https://en.wikipedia.org/wiki/Special:Search
Donate	https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en
Create account	https://en.wikipedia.org/w/index.php?title=Special:CreateAccount&returnto=Triangular+number
Log in	https://en.wikipedia.org/w/index.php?title=Special:UserLogin&returnto=Triangular+number
Donate	https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en
Create account	https://en.wikipedia.org/w/index.php?title=Special:CreateAccount&returnto=Triangular+number
Log in	https://en.wikipedia.org/w/index.php?title=Special:UserLogin&returnto=Triangular+number
(Top)	https://en.wikipedia.org/wiki/Triangular_number
1 Formula	https://en.wikipedia.org/wiki/Triangular_number#Formula
2 Relations to other figurate numbers	https://en.wikipedia.org/wiki/Triangular_number#Relations_to_other_figurate_numbers
3 Other properties	https://en.wikipedia.org/wiki/Triangular_number#Other_properties
4 Applications	https://en.wikipedia.org/wiki/Triangular_number#Applications
5 Triangular roots and tests for triangular numbers	https://en.wikipedia.org/wiki/Triangular_number#Triangular_roots_and_tests_for_triangular_numbers
6 Alternative name	https://en.wikipedia.org/wiki/Triangular_number#Alternative_name
7 See also	https://en.wikipedia.org/wiki/Triangular_number#See_also
8 References	https://en.wikipedia.org/wiki/Triangular_number#References
9 External links	https://en.wikipedia.org/wiki/Triangular_number#External_links
中文	https://zh.wikipedia.org/wiki/%E4%B8%89%E8%A7%92%E5%BD%A2%E6%95%B8
Français	https://fr.wikipedia.org/wiki/Nombre_triangulaire
עברית	https://he.wikipedia.org/wiki/%D7%9E%D7%A1%D7%A4%D7%A8_%D7%9E%D7%A9%D7%95%D7%9C%D7%A9%D7%99
한국어	https://ko.wikipedia.org/wiki/%EC%82%BC%EA%B0%81%EC%88%98
Español	https://es.wikipedia.org/wiki/N%C3%BAmero_triangular
தமிழ்	https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AF%81%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AF%8B%E0%AE%A3_%E0%AE%8E%E0%AE%A3%E0%AF%8D
Magyar	https://hu.wikipedia.org/wiki/H%C3%A1romsz%C3%B6gsz%C3%A1mok
Italiano	https://it.wikipedia.org/wiki/Numero_triangolare
Deutsch	https://de.wikipedia.org/wiki/Dreieckszahl
日本語	https://ja.wikipedia.org/wiki/%E4%B8%89%E8%A7%92%E6%95%B0
Tiếng Việt	https://vi.wikipedia.org/wiki/S%E1%BB%91_tam_gi%C3%A1c
Simple English	https://simple.wikipedia.org/wiki/Triangular_number
Nederlands	https://nl.wikipedia.org/wiki/Driehoeksgetal
Svenska	https://sv.wikipedia.org/wiki/Triangeltal
Português	https://pt.wikipedia.org/wiki/N%C3%BAmero_triangular
Íslenska	https://is.wikipedia.org/wiki/%C3%9Er%C3%ADhyrningstala
Русский	https://ru.wikipedia.org/wiki/%D0%A2%D1%80%D0%B5%D1%83%D0%B3%D0%BE%D0%BB%D1%8C%D0%BD%D0%BE%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE
Türkçe	https://tr.wikipedia.org/wiki/%C3%9C%C3%A7gensel_say%C4%B1
Română	https://ro.wikipedia.org/wiki/Num%C4%83r_triunghiular
Norsk bokmål	https://no.wikipedia.org/wiki/Trekanttall
Català	https://ca.wikipedia.org/wiki/Nombre_triangular
Suomi	https://fi.wikipedia.org/wiki/Kolmioluku
Українська	https://uk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%BA%D1%83%D1%82%D0%BD%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE
Latina	https://la.wikipedia.org/wiki/Numerus_triangularis
Slovenščina	https://sl.wikipedia.org/wiki/Trikotni%C5%A1ko_%C5%A1tevilo
Čeština	https://cs.wikipedia.org/wiki/Troj%C3%BAheln%C3%ADkov%C3%A9_%C4%8D%C3%ADslo
Dansk	https://da.wikipedia.org/wiki/Trekanttal
Azərbaycanca	https://az.wikipedia.org/wiki/%C3%9C%C3%A7bucaq_%C9%99d%C9%99dl%C9%99ri
فارسی	https://fa.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D9%85%D8%AB%D9%84%D8%AB%DB%8C
हिन्दी	https://hi.wikipedia.org/wiki/%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%95%E0%A5%8B%E0%A4%A3_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE
Српски / srpski	https://sr.wikipedia.org/wiki/%D0%A2%D1%80%D0%BE%D1%83%D0%B3%D0%B0%D0%BE%D0%BD%D0%B8_%D0%B1%D1%80%D0%BE%D1%98
ไทย	https://th.wikipedia.org/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B8%AA%E0%B8%B2%E0%B8%A1%E0%B9%80%E0%B8%AB%E0%B8%A5%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%A1
Esperanto	https://eo.wikipedia.org/wiki/Triangula_nombro
Български	https://bg.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D1%8A%D0%B3%D1%8A%D0%BB%D0%BD%D0%BE_%D1%87%D0%B8%D1%81%D0%BB%D0%BE
کوردی	https://ckb.wikipedia.org/wiki/%DA%98%D9%85%D8%A7%D8%B1%DB%95%DB%8C_%D8%B3%DB%8E%DA%AF%DB%86%D8%B4%DB%95%DB%8C%DB%8C
Emiliàn e rumagnòl	https://eml.wikipedia.org/wiki/N%C3%B9mer_triangol%C3%A8r
ਪੰਜਾਬੀ	https://pa.wikipedia.org/wiki/%E0%A8%A4%E0%A8%BF%E0%A8%95%E0%A9%8B%E0%A8%A3%E0%A9%80%E0%A8%86_%E0%A8%B8%E0%A9%B0%E0%A8%96%E0%A8%BF%E0%A8%86
Nordfriisk	https://frr.wikipedia.org/wiki/Triihuktaal
العربية	https://ar.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D9%85%D8%AB%D9%84%D8%AB%D9%8A
Slovenčina	https://sk.wikipedia.org/wiki/Trojuholn%C3%ADkov%C3%A9_%C4%8D%C3%ADslo
Bahasa Indonesia	https://id.wikipedia.org/wiki/Bilangan_segitiga
粵語	https://zh-yue.wikipedia.org/wiki/%E4%B8%89%E8%A7%92%E5%BD%A2%E6%95%B8
Oʻzbekcha / ўзбекча	https://uz.wikipedia.org/wiki/Uchburchak_sonlari
Galego	https://gl.wikipedia.org/wiki/N%C3%BAmero_triangular
Polski	https://pl.wikipedia.org/wiki/Liczby_tr%C3%B3jk%C4%85tne
বাংলা	https://bn.wikipedia.org/wiki/%E0%A6%A4%E0%A7%8D%E0%A6%B0%E0%A6%BF%E0%A6%AD%E0%A7%81%E0%A6%9C%E0%A6%BE%E0%A6%95%E0%A6%BE%E0%A6%B0_%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE
Bahasa Melayu	https://ms.wikipedia.org/wiki/Nombor_segi_tiga
Bosanski	https://bs.wikipedia.org/wiki/Trougaoni_brojevi
Ελληνικά	https://el.wikipedia.org/wiki/%CE%A4%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF%CF%82_%CE%B1%CF%81%CE%B9%CE%B8%CE%BC%CF%8C%CF%82
Edit links	https://www.wikidata.org/wiki/Special:EntityPage/Q245102#sitelinks-wikipedia
Article	https://en.wikipedia.org/wiki/Triangular_number
Talk	https://en.wikipedia.org/wiki/Talk:Triangular_number
Read	https://en.wikipedia.org/wiki/Triangular_number
Edit	https://en.wikipedia.org/w/index.php?title=Triangular_number&action=edit
View history	https://en.wikipedia.org/w/index.php?title=Triangular_number&action=history
Read	https://en.wikipedia.org/wiki/Triangular_number
Edit	https://en.wikipedia.org/w/index.php?title=Triangular_number&action=edit
View history	https://en.wikipedia.org/w/index.php?title=Triangular_number&action=history
What links here	https://en.wikipedia.org/wiki/Special:WhatLinksHere/Triangular_number
Related changes	https://en.wikipedia.org/wiki/Special:RecentChangesLinked/Triangular_number
Upload file	https://en.wikipedia.org/wiki/Wikipedia:File_Upload_Wizard
Permanent link	https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1331878442
Page information	https://en.wikipedia.org/w/index.php?title=Triangular_number&action=info
Cite this page	https://en.wikipedia.org/w/index.php?title=Special:CiteThisPage&page=Triangular_number&id=1331878442&wpFormIdentifier=titleform
Get shortened URL	https://en.wikipedia.org/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FTriangular_number
Download QR code	https://en.wikipedia.org/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FTriangular_number
Download as PDF	https://en.wikipedia.org/w/index.php?title=Special:DownloadAsPdf&page=Triangular_number&action=show-download-screen
Printable version	https://en.wikipedia.org/w/index.php?title=Triangular_number&printable=yes
Wikimedia Commons	https://commons.wikimedia.org/wiki/Category:Triangular_numbers
Wikifunctions	https://www.wikifunctions.org/wiki/Z13961
Wikidata item	https://www.wikidata.org/wiki/Special:EntityPage/Q245102
	https://en.wikipedia.org/wiki/File:First_six_triangular_numbers.svg
	https://en.wikipedia.org/wiki/File:Triangular_Numbers_Plot.svg
equilateral triangle	https://en.wikipedia.org/wiki/Equilateral_triangle
figurate number	https://en.wikipedia.org/wiki/Figurate_number
square numbers	https://en.wikipedia.org/wiki/Square_number
cube numbers	https://en.wikipedia.org/wiki/Cube_(algebra)#In_integers
natural numbers	https://en.wikipedia.org/wiki/Natural_number
sequence	https://en.wikipedia.org/wiki/Integer_sequence
0th triangular number	https://en.wikipedia.org/wiki/Empty_sum
A000217	https://oeis.org/A000217
OEIS	https://en.wikipedia.org/wiki/On-Line_Encyclopedia_of_Integer_Sequences
edit	https://en.wikipedia.org/w/index.php?title=Triangular_number&action=edit§ion=1
	https://en.wikipedia.org/wiki/File:Pascal_triangle_simplex_numbers.svg
Pascal's triangle	https://en.wikipedia.org/wiki/Pascal%27s_triangle
Natural numbers	https://en.wikipedia.org/wiki/Natural_number
Tetrahedral numbers	https://en.wikipedia.org/wiki/Tetrahedral_number
Pentatope numbers	https://en.wikipedia.org/wiki/Pentatope_number
5-simplex	https://en.wikipedia.org/wiki/5-simplex
6-simplex	https://en.wikipedia.org/wiki/6-simplex
7-simplex	https://en.wikipedia.org/wiki/7-simplex
binomial coefficient	https://en.wikipedia.org/wiki/Binomial_coefficient
visual proof	https://en.wikipedia.org/wiki/Proof_without_words
[1]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-1
	https://en.wikipedia.org/wiki/File:Illustration_of_Triangular_Number_T_4_Leading_to_a_Rectangle_(yellow-green).svg
mathematical induction	https://en.wikipedia.org/wiki/Mathematical_induction
[2]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-2
Gauss	https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss
[3]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-Gauss-3
Pythagoreans	https://en.wikipedia.org/wiki/Pythagoreans
[4]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-4
Dicuil	https://en.wikipedia.org/wiki/Dicuil
Computus	https://en.wikipedia.org/wiki/Computus
[5]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-5
[6]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-6
integer overflow	https://en.wikipedia.org/wiki/Integer_overflow
8-bit byte	https://en.wikipedia.org/wiki/8-bit_byte
conditional branch	https://en.wikipedia.org/wiki/Conditional_branch
binary OR	https://en.wikipedia.org/wiki/Binary_OR
truncated away	https://en.wikipedia.org/wiki/Division_(mathematics)#Of_integers
edit	https://en.wikipedia.org/w/index.php?title=Triangular_number&action=edit§ion=2
[7]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-7
[8]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-8
Theon of Smyrna	https://en.wikipedia.org/wiki/Theon_of_Smyrna
[9]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-9
digit sums	https://en.wikipedia.org/wiki/Digit_sum
	https://en.wikipedia.org/wiki/File:Square_number_16_as_sum_of_two_triangular_numbers.svg
	https://en.wikipedia.org/wiki/File:Square_number_25_as_sum_of_two_triangular_numbers.svg
§ Formula	https://en.wikipedia.org/wiki/Triangular_number#Formula
pronic number	https://en.wikipedia.org/wiki/Pronic_number
triangular numbers that are also square numbers	https://en.wikipedia.org/wiki/Square_triangular_number
	https://en.wikipedia.org/wiki/File:Nicomachus_theorem_3D.svg
square of the nth triangular number	https://en.wikipedia.org/wiki/Squared_triangular_number
	https://en.wikipedia.org/wiki/File:Visual_proof_tetrahedral_number.svg
[10]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-10
tetrahedral number	https://en.wikipedia.org/wiki/Tetrahedral_number
m-gonal number	https://en.wikipedia.org/wiki/Polygonal_number
heptagonal number	https://en.wikipedia.org/wiki/Heptagonal_number
hexagonal number	https://en.wikipedia.org/wiki/Hexagonal_number
centered polygonal number	https://en.wikipedia.org/wiki/Centered_polygonal_number
trapezoidal number	https://en.wikipedia.org/wiki/Trapezoidal_number
binomial coefficients	https://en.wikipedia.org/wiki/Binomial_coefficient
[11]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-11
	https://en.wikipedia.org/wiki/File:Tetrahedral_triangular_number_10.svg
Pascal's triangle	https://en.wikipedia.org/wiki/Pascal%27s_triangle
pentatope number	https://en.wikipedia.org/wiki/Pentatope_number
edit	https://en.wikipedia.org/w/index.php?title=Triangular_number&action=edit§ion=3
Faulhaber's formula	https://en.wikipedia.org/wiki/Faulhaber%27s_formula
	https://en.wikipedia.org/wiki/File:Hexagonal_number_visual_proof.svg
	https://en.wikipedia.org/wiki/File:Hexagonal_number_visual_proof.svg
	https://en.wikipedia.org/wiki/File:Hexagonal_number_visual_proof.svg
Proof without words	https://en.wikipedia.org/wiki/Proof_without_words
perfect number	https://en.wikipedia.org/wiki/Perfect_number
Mersenne prime	https://en.wikipedia.org/wiki/Mersenne_prime
base 10	https://en.wikipedia.org/wiki/Base_10
digital root	https://en.wikipedia.org/wiki/Digital_root
reciprocals	https://en.wikipedia.org/wiki/Multiplicative_inverse
telescoping series	https://en.wikipedia.org/wiki/Telescoping_series
ΕΥΡΗΚΑ!	https://en.wikipedia.org/wiki/Eureka_(word)
Fermat polygonal number theorem	https://en.wikipedia.org/wiki/Fermat_polygonal_number_theorem
4095	https://en.wikipedia.org/wiki/4000_(number)#4001_to_4099
Ramanujan–Nagell equation	https://en.wikipedia.org/wiki/Ramanujan%E2%80%93Nagell_equation
Wacław Franciszek Sierpiński	https://en.wikipedia.org/wiki/Wac%C5%82aw_Sierpi%C5%84ski
geometric progression	https://en.wikipedia.org/wiki/Geometric_progression
Kazimierz Szymiczek	https://en.wikipedia.org/w/index.php?title=Kazimierz_Szymiczek&action=edit&redlink=1
[12]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-12
[13]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-13
theta functions	https://en.wikipedia.org/wiki/Theta_function
Ramanujan theta function	https://en.wikipedia.org/wiki/Ramanujan_theta_function
[14]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-14
[15]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-15
recurrence relation	https://en.wikipedia.org/wiki/Recurrence_relation
limit	https://en.wikipedia.org/wiki/Limit_of_a_sequence
edit	https://en.wikipedia.org/w/index.php?title=Triangular_number&action=edit§ion=4
	https://en.wikipedia.org/wiki/File:Handshake_problem_visual_proof.svg
Proof without words	https://en.wikipedia.org/wiki/Proof_without_words
[16]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-16
fully connected network	https://en.wikipedia.org/wiki/Fully_connected_network
[17]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-17
group stage	https://en.wikipedia.org/wiki/Group_stage
	https://en.wikipedia.org/wiki/File:Central_polygonal_numbers.svg
depreciation	https://en.wikipedia.org/wiki/Depreciation
sum-of-years' digits method	https://en.wikipedia.org/wiki/Depreciation#Sum-of-years-digits_method
Board game	https://en.wikipedia.org/wiki/Board_game
game designers	https://en.wikipedia.org/wiki/Game_design
[18]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-18
domino	https://en.wikipedia.org/wiki/Domino
edit	https://en.wikipedia.org/w/index.php?title=Triangular_number&action=edit§ion=5
square root	https://en.wikipedia.org/wiki/Square_root
[19]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-EulerRoots-19
quadratic formula	https://en.wikipedia.org/wiki/Quadratic_formula
if and only if	https://en.wikipedia.org/wiki/If_and_only_if
[19]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-EulerRoots-19
edit	https://en.wikipedia.org/w/index.php?title=Triangular_number&action=edit§ion=6
factorial	https://en.wikipedia.org/wiki/Factorial
Donald Knuth	https://en.wikipedia.org/wiki/Donald_Knuth
[20]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-20
[21]	https://en.wikipedia.org/wiki/Triangular_number#cite_note-21
edit	https://en.wikipedia.org/w/index.php?title=Triangular_number&action=edit§ion=7
1 + 2 + 3 + 4 + ⋯	https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
Doubly triangular number	https://en.wikipedia.org/wiki/Doubly_triangular_number
Tetractys	https://en.wikipedia.org/wiki/Tetractys
Factoriangular number	https://en.wikipedia.org/wiki/Factoriangular_number
Šindel sequence	https://en.wikipedia.org/wiki/%C5%A0indel_sequence
edit	https://en.wikipedia.org/w/index.php?title=Triangular_number&action=edit§ion=8
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-1
"Triangular Number Sequence"	https://www.mathsisfun.com/algebra/triangular-numbers.html
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-2
Spivak, Michael	https://en.wikipedia.org/wiki/Michael_Spivak
Calculus	https://books.google.com/books?id=7JKVu_9InRUC&pg=PA21
ISBN	https://en.wikipedia.org/wiki/ISBN_(identifier)
978-0-914098-91-1	https://en.wikipedia.org/wiki/Special:BookSources/978-0-914098-91-1
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-Gauss_3-0
"Gauss's Day of Reckoning"	https://web.archive.org/web/20150402141244/http://www.americanscientist.org/issues/pub/gausss-day-of-reckoning/1
the original	http://www.americanscientist.org/issues/pub/gausss-day-of-reckoning/1
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-4
"Webpage cites AN INTRODUCTION TO THE HISTORY OF MATHEMATICS"	http://mathcentral.uregina.ca/QQ/database/QQ.09.98/matt1.html
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-5
Esposito, Mario	https://en.wikipedia.org/wiki/Mario_Esposito_(scholar)
"An unpublished astronomical treatise by the Irish monk Dicuil"	https://archive.org/details/proceedingsofroy2619roya
Proceedings of the Royal Irish Academy, Section C	https://en.wikipedia.org/wiki/Proceedings_of_the_Royal_Irish_Academy,_Section_C
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-6
"Dicuil (9th century) on triangular and square numbers"	https://dspace.stir.ac.uk/handle/1893/29437
doi	https://en.wikipedia.org/wiki/Doi_(identifier)
10.1080/26375451.2019.1598687	https://doi.org/10.1080%2F26375451.2019.1598687
hdl	https://en.wikipedia.org/wiki/Hdl_(identifier)
1893/29437	https://hdl.handle.net/1893%2F29437
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-7
"Triangular Numbers and Perfect Squares"	https://doi.org/10.2307/3621134
doi	https://en.wikipedia.org/wiki/Doi_(identifier)
10.2307/3621134	https://doi.org/10.2307%2F3621134
JSTOR	https://en.wikipedia.org/wiki/JSTOR_(identifier)
3621134	https://www.jstor.org/stable/3621134
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-8
"Triangular Number"	https://mathworld.wolfram.com/TriangularNumber.html
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-9
Algebra in Context: Introductory Algebra from Origins to Applications	https://doi.org/10.1353/book.49475
doi	https://en.wikipedia.org/wiki/Doi_(identifier)
10.1353/book.49475	https://doi.org/10.1353%2Fbook.49475
ISBN	https://en.wikipedia.org/wiki/ISBN_(identifier)
9781421417288	https://en.wikipedia.org/wiki/Special:BookSources/9781421417288
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-10
http://demonstrations.wolfram.com/GeometricProofOfTheTetrahedralNumberFormula	http://demonstrations.wolfram.com/GeometricProofOfTheTetrahedralNumberFormula
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-11
"Die k-dimensionale Champagnerpyramide"	https://epub.uni-bayreuth.de/3850/1/Baumann_Champagnerpyramide.pdf
doi	https://en.wikipedia.org/wiki/Doi_(identifier)
10.1007/s00591-018-00236-x	https://doi.org/10.1007%2Fs00591-018-00236-x
ISSN	https://en.wikipedia.org/wiki/ISSN_(identifier)
1432-1815	https://search.worldcat.org/issn/1432-1815
S2CID	https://en.wikipedia.org/wiki/S2CID_(identifier)
125426184	https://api.semanticscholar.org/CorpusID:125426184
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-12
Chen, Fang: Triangular numbers in geometric progression	http://www.emis.de/journals/INTEGERS/papers/h19/h19.pdf
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-13
Fang: Nonexistence of a geometric progression that contains four triangular numbers	http://www.emis.de/journals/INTEGERS/papers/h57/h57.pdf
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-14
doi	https://en.wikipedia.org/wiki/Doi_(identifier)
10.1023/B:RAMA.0000012425.42327.ae	https://doi.org/10.1023%2FB%3ARAMA.0000012425.42327.ae
ISSN	https://en.wikipedia.org/wiki/ISSN_(identifier)
1382-4090	https://search.worldcat.org/issn/1382-4090
S2CID	https://en.wikipedia.org/wiki/S2CID_(identifier)
122221070	https://api.semanticscholar.org/CorpusID:122221070
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-15
arXiv	https://en.wikipedia.org/wiki/ArXiv_(identifier)
1601.06378	https://arxiv.org/abs/1601.06378
math.NT	https://arxiv.org/archive/math.NT
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-16
"The Handshake Problem \| National Association of Math Circles"	https://web.archive.org/web/20160310182700/http://www.mathcircles.org/node/835
the original	http://www.mathcircles.org/node/835
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-17
"The Lost 4-Dimensional Rotation"	https://henders.one/2022/05/09/lost-4D-rotation/
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-18
Building Blocks of Tabletop Game Design	https://dx.doi.org/10.1201/9780429430701
doi	https://en.wikipedia.org/wiki/Doi_(identifier)
10.1201/9780429430701	https://doi.org/10.1201%2F9780429430701
ISBN	https://en.wikipedia.org/wiki/ISBN_(identifier)
978-0-429-43070-1	https://en.wikipedia.org/wiki/Special:BookSources/978-0-429-43070-1
S2CID	https://en.wikipedia.org/wiki/S2CID_(identifier)
198342061	https://api.semanticscholar.org/CorpusID:198342061
a	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-EulerRoots_19-0
b	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-EulerRoots_19-1
Euler, Leonhard	https://en.wikipedia.org/wiki/Leonhard_Euler
Lagrange, Joseph Louis	https://en.wikipedia.org/wiki/Joseph_Louis_Lagrange
Elements of Algebra	https://en.wikipedia.org/wiki/Elements_of_Algebra
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-20
Knuth, Donald	https://en.wikipedia.org/wiki/Donald_Knuth
The Art of Computer Programming	https://en.wikipedia.org/wiki/The_Art_of_Computer_Programming
^	https://en.wikipedia.org/wiki/Triangular_number#cite_ref-21
doi	https://en.wikipedia.org/wiki/Doi_(identifier)
10.1007/978-3-662-57970-1	https://doi.org/10.1007%2F978-3-662-57970-1
ISBN	https://en.wikipedia.org/wiki/ISBN_(identifier)
978-3-662-57968-8	https://en.wikipedia.org/wiki/Special:BookSources/978-3-662-57968-8
S2CID	https://en.wikipedia.org/wiki/S2CID_(identifier)
53079729	https://api.semanticscholar.org/CorpusID:53079729
edit	https://en.wikipedia.org/w/index.php?title=Triangular_number&action=edit§ion=9
	https://en.wikipedia.org/wiki/File:Commons-logo.svg
triangular numbers	https://commons.wikimedia.org/wiki/Category:Triangular_numbers
"Arithmetic series"	https://www.encyclopediaofmath.org/index.php?title=Arithmetic_series
Encyclopedia of Mathematics	https://en.wikipedia.org/wiki/Encyclopedia_of_Mathematics
EMS Press	https://en.wikipedia.org/wiki/European_Mathematical_Society
Triangular numbers	http://www.cut-the-knot.org/do_you_know/numbers.shtml#square
cut-the-knot	https://en.wikipedia.org/wiki/Cut-the-knot
There exist triangular numbers that are also square	http://www.cut-the-knot.org/do_you_know/triSquare.shtml
cut-the-knot	https://en.wikipedia.org/wiki/Cut-the-knot
Weisstein, Eric W.	https://en.wikipedia.org/wiki/Eric_W._Weisstein
"Triangular Number"	https://mathworld.wolfram.com/TriangularNumber.html
MathWorld	https://en.wikipedia.org/wiki/MathWorld
Hypertetrahedral Polytopic Roots	http://rhubbarb.wordpress.com/2009/04/23/hypertetrahedral-polytopic-roots/
v	https://en.wikipedia.org/wiki/Template:Figurate_numbers
t	https://en.wikipedia.org/wiki/Template_talk:Figurate_numbers
e	https://en.wikipedia.org/wiki/Special:EditPage/Template:Figurate_numbers
Figurate numbers	https://en.wikipedia.org/wiki/Figurate_number
2-dimensional	https://en.wikipedia.org/wiki/Plane_(mathematics)
centered	https://en.wikipedia.org/wiki/Centered_polygonal_number
Centered triangular numbers	https://en.wikipedia.org/wiki/Centered_triangular_number
Centered square numbers	https://en.wikipedia.org/wiki/Centered_square_number
Centered pentagonal numbers	https://en.wikipedia.org/wiki/Centered_pentagonal_number
Centered hexagonal numbers	https://en.wikipedia.org/wiki/Centered_hexagonal_number
Centered heptagonal numbers	https://en.wikipedia.org/wiki/Centered_heptagonal_number
Centered octagonal numbers	https://en.wikipedia.org/wiki/Centered_octagonal_number
Centered nonagonal numbers	https://en.wikipedia.org/wiki/Centered_nonagonal_number
Centered decagonal numbers	https://en.wikipedia.org/wiki/Centered_decagonal_number
Star numbers	https://en.wikipedia.org/wiki/Star_number
non-centered	https://en.wikipedia.org/wiki/Polygonal_number
Square numbers	https://en.wikipedia.org/wiki/Square_number
Pentagonal numbers	https://en.wikipedia.org/wiki/Pentagonal_number
Hexagonal numbers	https://en.wikipedia.org/wiki/Hexagonal_number
Heptagonal numbers	https://en.wikipedia.org/wiki/Heptagonal_number
Octagonal numbers	https://en.wikipedia.org/wiki/Octagonal_number
Nonagonal numbers	https://en.wikipedia.org/wiki/Nonagonal_number
Decagonal numbers	https://en.wikipedia.org/wiki/Decagonal_number
Dodecagonal numbers	https://en.wikipedia.org/wiki/Dodecagonal_number
3-dimensional	https://en.wikipedia.org/wiki/Three-dimensional_space
centered	https://en.wikipedia.org/wiki/Centered_polyhedral_number
Centered tetrahedral numbers	https://en.wikipedia.org/wiki/Centered_tetrahedral_number
Centered cube numbers	https://en.wikipedia.org/wiki/Centered_cube_number
Centered octahedral numbers	https://en.wikipedia.org/wiki/Centered_octahedral_number
Centered dodecahedral numbers	https://en.wikipedia.org/wiki/Centered_dodecahedral_number
Centered icosahedral numbers	https://en.wikipedia.org/wiki/Centered_icosahedral_number
non-centered	https://en.wikipedia.org/wiki/Polyhedral_number
Cube numbers	https://en.wikipedia.org/wiki/Cube_(algebra)
Octahedral numbers	https://en.wikipedia.org/wiki/Octahedral_number
Dodecahedral numbers	https://en.wikipedia.org/wiki/Dodecahedral_number
Icosahedral numbers	https://en.wikipedia.org/wiki/Icosahedral_number
Stella octangula numbers	https://en.wikipedia.org/wiki/Stella_octangula_number
pyramidal	https://en.wikipedia.org/wiki/Pyramidal_number
Tetrahedral numbers	https://en.wikipedia.org/wiki/Tetrahedral_number
Square pyramidal numbers	https://en.wikipedia.org/wiki/Square_pyramidal_number
4-dimensional	https://en.wikipedia.org/wiki/Four-dimensional_space
Pentatope numbers	https://en.wikipedia.org/wiki/Pentatope_number
Squared triangular numbers	https://en.wikipedia.org/wiki/Squared_triangular_number
Tesseractic numbers	https://en.wikipedia.org/wiki/Fourth_power
dimensional	https://en.wikipedia.org/wiki/Dimension
5-hypercube numbers	https://en.wikipedia.org/wiki/Fifth_power_(algebra)
6-hypercube numbers	https://en.wikipedia.org/wiki/Sixth_power
7-hypercube numbers	https://en.wikipedia.org/wiki/Seventh_power
8-hypercube numbers	https://en.wikipedia.org/wiki/Eighth_power
v	https://en.wikipedia.org/wiki/Template:Series_(mathematics)
t	https://en.wikipedia.org/wiki/Template_talk:Series_(mathematics)
e	https://en.wikipedia.org/wiki/Special:EditPage/Template:Series_(mathematics)
Sequences	https://en.wikipedia.org/wiki/Sequence
series	https://en.wikipedia.org/wiki/Series_(mathematics)
List of mathematical series	https://en.wikipedia.org/wiki/List_of_mathematical_series
Integer sequences	https://en.wikipedia.org/wiki/Integer_sequence
Arithmetic progression	https://en.wikipedia.org/wiki/Arithmetic_progression
Geometric progression	https://en.wikipedia.org/wiki/Geometric_progression
Harmonic progression	https://en.wikipedia.org/wiki/Harmonic_progression_(mathematics)
Square number	https://en.wikipedia.org/wiki/Square_number
Cubic number	https://en.wikipedia.org/wiki/Cube_(algebra)
Factorial	https://en.wikipedia.org/wiki/Factorial
Powers of two	https://en.wikipedia.org/wiki/Power_of_two
Powers of three	https://en.wikipedia.org/wiki/Power_of_three
Powers of 10	https://en.wikipedia.org/wiki/Power_of_10
list	https://en.wikipedia.org/wiki/List_of_OEIS_sequences
Complete sequence	https://en.wikipedia.org/wiki/Complete_sequence
Fibonacci sequence	https://en.wikipedia.org/wiki/Fibonacci_sequence
Figurate number	https://en.wikipedia.org/wiki/Figurate_number
Heptagonal number	https://en.wikipedia.org/wiki/Heptagonal_number
Hexagonal number	https://en.wikipedia.org/wiki/Hexagonal_number
Lucas number	https://en.wikipedia.org/wiki/Lucas_number
Pell number	https://en.wikipedia.org/wiki/Pell_number
Pentagonal number	https://en.wikipedia.org/wiki/Pentagonal_number
Polygonal number	https://en.wikipedia.org/wiki/Polygonal_number
array	https://en.wikipedia.org/wiki/Triangular_array
	https://en.wikipedia.org/wiki/Fibonacci_sequence
Cauchy sequence	https://en.wikipedia.org/wiki/Cauchy_sequence
Monotonic function	https://en.wikipedia.org/wiki/Monotonic_function
Periodic sequence	https://en.wikipedia.org/wiki/Periodic_sequence
Alternating	https://en.wikipedia.org/wiki/Alternating_series
Convergent	https://en.wikipedia.org/wiki/Convergent_series
Divergent	https://en.wikipedia.org/wiki/Divergent_series
Telescoping	https://en.wikipedia.org/wiki/Telescoping_series
Absolute	https://en.wikipedia.org/wiki/Absolute_convergence
Conditional	https://en.wikipedia.org/wiki/Conditional_convergence
Uniform	https://en.wikipedia.org/wiki/Uniform_convergence
1/2 − 1/4 + 1/8 − 1/16 + ⋯	https://en.wikipedia.org/wiki/1/2_%E2%88%92_1/4_%2B_1/8_%E2%88%92_1/16_%2B_%E2%8B%AF
1/2 + 1/4 + 1/8 + 1/16 + ⋯	https://en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/16_%2B_%E2%8B%AF
1/4 + 1/16 + 1/64 + 1/256 + ⋯	https://en.wikipedia.org/wiki/1/4_%2B_1/16_%2B_1/64_%2B_1/256_%2B_%E2%8B%AF
1 + 1/2s + 1/3s + ... (Riemann zeta function)	https://en.wikipedia.org/wiki/Riemann_zeta_function
1 + 1 + 1 + 1 + ⋯	https://en.wikipedia.org/wiki/1_%2B_1_%2B_1_%2B_1_%2B_%E2%8B%AF
1 − 1 + 1 − 1 + ⋯ (Grandi's series)	https://en.wikipedia.org/wiki/Grandi%27s_series
1 + 2 + 3 + 4 + ⋯	https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
1 − 2 + 3 − 4 + ⋯	https://en.wikipedia.org/wiki/1_%E2%88%92_2_%2B_3_%E2%88%92_4_%2B_%E2%8B%AF
1 + 2 + 4 + 8 + ⋯	https://en.wikipedia.org/wiki/1_%2B_2_%2B_4_%2B_8_%2B_%E2%8B%AF
1 − 2 + 4 − 8 + ⋯	https://en.wikipedia.org/wiki/1_%E2%88%92_2_%2B_4_%E2%88%92_8_%2B_%E2%8B%AF
Infinite arithmetic series	https://en.wikipedia.org/wiki/Infinite_arithmetic_series
1 − 1 + 2 − 6 + 24 − 120 + ⋯ (alternating factorials)	https://en.wikipedia.org/wiki/1_%E2%88%92_1_%2B_2_%E2%88%92_6_%2B_24_%E2%88%92_120_%2B_%E2%8B%AF
1 + 1/2 + 1/3 + 1/4 + ⋯ (harmonic series)	https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)
1/2 + 1/3 + 1/5 + 1/7 + 1/11 + ⋯ (inverses of primes)	https://en.wikipedia.org/wiki/Divergence_of_the_sum_of_the_reciprocals_of_the_primes
Taylor series	https://en.wikipedia.org/wiki/Taylor_series
Power series	https://en.wikipedia.org/wiki/Power_series
Formal power series	https://en.wikipedia.org/wiki/Formal_power_series
Laurent series	https://en.wikipedia.org/wiki/Laurent_series
Puiseux series	https://en.wikipedia.org/wiki/Puiseux_series
Dirichlet series	https://en.wikipedia.org/wiki/Dirichlet_series
Trigonometric series	https://en.wikipedia.org/wiki/Trigonometric_series
Fourier series	https://en.wikipedia.org/wiki/Fourier_series
Generating series	https://en.wikipedia.org/wiki/Generating_series
Hypergeometric series	https://en.wikipedia.org/wiki/Hypergeometric_function
Generalized hypergeometric series	https://en.wikipedia.org/wiki/Generalized_hypergeometric_series
Hypergeometric function of a matrix argument	https://en.wikipedia.org/wiki/Hypergeometric_function_of_a_matrix_argument
Lauricella hypergeometric series	https://en.wikipedia.org/wiki/Lauricella_hypergeometric_series
Modular hypergeometric series	https://en.wikipedia.org/wiki/Modular_hypergeometric_series
Riemann's differential equation	https://en.wikipedia.org/wiki/Riemann%27s_differential_equation
Theta hypergeometric series	https://en.wikipedia.org/wiki/Theta_hypergeometric_series
Category	https://en.wikipedia.org/wiki/Category:Series_(mathematics)
v	https://en.wikipedia.org/wiki/Template:Classes_of_natural_numbers
t	https://en.wikipedia.org/wiki/Template_talk:Classes_of_natural_numbers
e	https://en.wikipedia.org/wiki/Special:EditPage/Template:Classes_of_natural_numbers
natural numbers	https://en.wikipedia.org/wiki/Natural_number
Powers	https://en.wikipedia.org/wiki/Exponentiation
Achilles	https://en.wikipedia.org/wiki/Achilles_number
Power of 2	https://en.wikipedia.org/wiki/Power_of_two
Power of 3	https://en.wikipedia.org/wiki/Power_of_three
Power of 10	https://en.wikipedia.org/wiki/Power_of_10
Square	https://en.wikipedia.org/wiki/Square_number
Cube	https://en.wikipedia.org/wiki/Cube_(algebra)
Fourth power	https://en.wikipedia.org/wiki/Fourth_power
Fifth power	https://en.wikipedia.org/wiki/Fifth_power_(algebra)
Sixth power	https://en.wikipedia.org/wiki/Sixth_power
Seventh power	https://en.wikipedia.org/wiki/Seventh_power
Eighth power	https://en.wikipedia.org/wiki/Eighth_power
Perfect power	https://en.wikipedia.org/wiki/Perfect_power
Powerful	https://en.wikipedia.org/wiki/Powerful_number
Prime power	https://en.wikipedia.org/wiki/Prime_power
Cullen	https://en.wikipedia.org/wiki/Cullen_number
Double Mersenne	https://en.wikipedia.org/wiki/Double_Mersenne_number
Fermat	https://en.wikipedia.org/wiki/Fermat_number
Mersenne	https://en.wikipedia.org/wiki/Mersenne_prime
Proth	https://en.wikipedia.org/wiki/Proth_number
Thabit	https://en.wikipedia.org/wiki/Thabit_number
Woodall	https://en.wikipedia.org/wiki/Woodall_number
Hilbert	https://en.wikipedia.org/wiki/Hilbert_number
Idoneal	https://en.wikipedia.org/wiki/Idoneal_number
Leyland	https://en.wikipedia.org/wiki/Leyland_number
Loeschian	https://en.wikipedia.org/wiki/Loeschian_number
Lucky numbers of Euler	https://en.wikipedia.org/wiki/Lucky_numbers_of_Euler
Recursively	https://en.wikipedia.org/wiki/Recursion
Fibonacci	https://en.wikipedia.org/wiki/Fibonacci_sequence
Jacobsthal	https://en.wikipedia.org/wiki/Jacobsthal_number
Leonardo	https://en.wikipedia.org/wiki/Leonardo_number
Lucas	https://en.wikipedia.org/wiki/Lucas_number
Narayana	https://en.wikipedia.org/wiki/Supergolden_ratio#Narayana_sequence
Padovan	https://en.wikipedia.org/wiki/Padovan_sequence
Pell	https://en.wikipedia.org/wiki/Pell_number
Perrin	https://en.wikipedia.org/wiki/Perrin_number
Graham	https://en.wikipedia.org/wiki/Graham%27s_number
Amenable	https://en.wikipedia.org/wiki/Amenable_number
Congruent	https://en.wikipedia.org/wiki/Congruent_number
Knödel	https://en.wikipedia.org/wiki/Kn%C3%B6del_number
Riesel	https://en.wikipedia.org/wiki/Riesel_number
Sierpiński	https://en.wikipedia.org/wiki/Sierpi%C5%84ski_number
Nonhypotenuse	https://en.wikipedia.org/wiki/Nonhypotenuse_number
Polite	https://en.wikipedia.org/wiki/Polite_number
Practical	https://en.wikipedia.org/wiki/Practical_number
Primary pseudoperfect	https://en.wikipedia.org/wiki/Primary_pseudoperfect_number
Ulam	https://en.wikipedia.org/wiki/Ulam_number
Wolstenholme	https://en.wikipedia.org/wiki/Wolstenholme_number
Figurate numbers	https://en.wikipedia.org/wiki/Figurate_number
2-dimensional	https://en.wikipedia.org/wiki/Plane_(mathematics)
centered	https://en.wikipedia.org/wiki/Centered_polygonal_number
Centered triangular	https://en.wikipedia.org/wiki/Centered_triangular_number
Centered square	https://en.wikipedia.org/wiki/Centered_square_number
Centered pentagonal	https://en.wikipedia.org/wiki/Centered_pentagonal_number
Centered hexagonal	https://en.wikipedia.org/wiki/Centered_hexagonal_number
Centered heptagonal	https://en.wikipedia.org/wiki/Centered_heptagonal_number
Centered octagonal	https://en.wikipedia.org/wiki/Centered_octagonal_number
Centered nonagonal	https://en.wikipedia.org/wiki/Centered_nonagonal_number
Centered decagonal	https://en.wikipedia.org/wiki/Centered_decagonal_number
Star	https://en.wikipedia.org/wiki/Star_number
non-centered	https://en.wikipedia.org/wiki/Polygonal_number
Square	https://en.wikipedia.org/wiki/Square_number
Square triangular	https://en.wikipedia.org/wiki/Square_triangular_number
Pentagonal	https://en.wikipedia.org/wiki/Pentagonal_number
Hexagonal	https://en.wikipedia.org/wiki/Hexagonal_number
Heptagonal	https://en.wikipedia.org/wiki/Heptagonal_number
Octagonal	https://en.wikipedia.org/wiki/Octagonal_number
Nonagonal	https://en.wikipedia.org/wiki/Nonagonal_number
Decagonal	https://en.wikipedia.org/wiki/Decagonal_number
Dodecagonal	https://en.wikipedia.org/wiki/Dodecagonal_number
3-dimensional	https://en.wikipedia.org/wiki/Three-dimensional_space
centered	https://en.wikipedia.org/wiki/Centered_polyhedral_number
Centered tetrahedral	https://en.wikipedia.org/wiki/Centered_tetrahedral_number
Centered cube	https://en.wikipedia.org/wiki/Centered_cube_number
Centered octahedral	https://en.wikipedia.org/wiki/Centered_octahedral_number
Centered dodecahedral	https://en.wikipedia.org/wiki/Centered_dodecahedral_number
Centered icosahedral	https://en.wikipedia.org/wiki/Centered_icosahedral_number
non-centered	https://en.wikipedia.org/wiki/Polyhedral_number
Tetrahedral	https://en.wikipedia.org/wiki/Tetrahedral_number
Cubic	https://en.wikipedia.org/wiki/Cube_(algebra)
Octahedral	https://en.wikipedia.org/wiki/Octahedral_number
Dodecahedral	https://en.wikipedia.org/wiki/Dodecahedral_number
Icosahedral	https://en.wikipedia.org/wiki/Icosahedral_number
Stella octangula	https://en.wikipedia.org/wiki/Stella_octangula_number
pyramidal	https://en.wikipedia.org/wiki/Pyramidal_number
Square pyramidal	https://en.wikipedia.org/wiki/Square_pyramidal_number
4-dimensional	https://en.wikipedia.org/wiki/Four-dimensional_space
Pentatope	https://en.wikipedia.org/wiki/Pentatope_number
Squared triangular	https://en.wikipedia.org/wiki/Squared_triangular_number
Tesseractic	https://en.wikipedia.org/wiki/Fourth_power
Bell	https://en.wikipedia.org/wiki/Bell_number
Cake	https://en.wikipedia.org/wiki/Cake_number
Catalan	https://en.wikipedia.org/wiki/Catalan_number
Dedekind	https://en.wikipedia.org/wiki/Dedekind_number
Delannoy	https://en.wikipedia.org/wiki/Delannoy_number
Euler	https://en.wikipedia.org/wiki/Euler_number
Eulerian	https://en.wikipedia.org/wiki/Eulerian_number
Fuss–Catalan	https://en.wikipedia.org/wiki/Fuss%E2%80%93Catalan_number
Lah	https://en.wikipedia.org/wiki/Lah_number
Lazy caterer's sequence	https://en.wikipedia.org/wiki/Lazy_caterer%27s_sequence
Lobb	https://en.wikipedia.org/wiki/Lobb_number
Motzkin	https://en.wikipedia.org/wiki/Motzkin_number
Narayana	https://en.wikipedia.org/wiki/Narayana_number
Ordered Bell	https://en.wikipedia.org/wiki/Ordered_Bell_number
Schröder	https://en.wikipedia.org/wiki/Schr%C3%B6der_number
Schröder–Hipparchus	https://en.wikipedia.org/wiki/Schr%C3%B6der%E2%80%93Hipparchus_number
Stirling first	https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind
Stirling second	https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind
Telephone number	https://en.wikipedia.org/wiki/Telephone_number_(mathematics)
Wedderburn–Etherington	https://en.wikipedia.org/wiki/Wedderburn%E2%80%93Etherington_number
Primes	https://en.wikipedia.org/wiki/Prime_number
Wieferich	https://en.wikipedia.org/wiki/Wieferich_prime#Wieferich_numbers
Wall–Sun–Sun	https://en.wikipedia.org/wiki/Wall%E2%80%93Sun%E2%80%93Sun_prime
Wolstenholme prime	https://en.wikipedia.org/wiki/Wolstenholme_prime
Wilson	https://en.wikipedia.org/wiki/Wilson_prime#Wilson_numbers
Pseudoprimes	https://en.wikipedia.org/wiki/Pseudoprime
Carmichael number	https://en.wikipedia.org/wiki/Carmichael_number
Catalan pseudoprime	https://en.wikipedia.org/wiki/Catalan_pseudoprime
Elliptic pseudoprime	https://en.wikipedia.org/wiki/Elliptic_pseudoprime
Euler pseudoprime	https://en.wikipedia.org/wiki/Euler_pseudoprime
Euler–Jacobi pseudoprime	https://en.wikipedia.org/wiki/Euler%E2%80%93Jacobi_pseudoprime
Fermat pseudoprime	https://en.wikipedia.org/wiki/Fermat_pseudoprime
Frobenius pseudoprime	https://en.wikipedia.org/wiki/Frobenius_pseudoprime
Lucas pseudoprime	https://en.wikipedia.org/wiki/Lucas_pseudoprime
Lucas–Carmichael number	https://en.wikipedia.org/wiki/Lucas%E2%80%93Carmichael_number
Perrin pseudoprime	https://en.wikipedia.org/wiki/Perrin_number#Perrin_primality_test
Somer–Lucas pseudoprime	https://en.wikipedia.org/wiki/Somer%E2%80%93Lucas_pseudoprime
Strong pseudoprime	https://en.wikipedia.org/wiki/Strong_pseudoprime
Arithmetic functions	https://en.wikipedia.org/wiki/Arithmetic_function
dynamics	https://en.wikipedia.org/wiki/Arithmetic_dynamics
Divisor functions	https://en.wikipedia.org/wiki/Divisor_function
Abundant	https://en.wikipedia.org/wiki/Abundant_number
Almost perfect	https://en.wikipedia.org/wiki/Almost_perfect_number
Arithmetic	https://en.wikipedia.org/wiki/Arithmetic_number
Betrothed	https://en.wikipedia.org/wiki/Betrothed_numbers
Colossally abundant	https://en.wikipedia.org/wiki/Colossally_abundant_number
Deficient	https://en.wikipedia.org/wiki/Deficient_number
Descartes	https://en.wikipedia.org/wiki/Descartes_number
Hemiperfect	https://en.wikipedia.org/wiki/Hemiperfect_number
Highly abundant	https://en.wikipedia.org/wiki/Highly_abundant_number
Highly composite	https://en.wikipedia.org/wiki/Highly_composite_number
Hyperperfect	https://en.wikipedia.org/wiki/Hyperperfect_number
Multiply perfect	https://en.wikipedia.org/wiki/Multiply_perfect_number
Perfect	https://en.wikipedia.org/wiki/Perfect_number
Practical	https://en.wikipedia.org/wiki/Practical_number
Primitive abundant	https://en.wikipedia.org/wiki/Primitive_abundant_number
Quasiperfect	https://en.wikipedia.org/wiki/Quasiperfect_number
Refactorable	https://en.wikipedia.org/wiki/Refactorable_number
Semiperfect	https://en.wikipedia.org/wiki/Semiperfect_number
Sublime	https://en.wikipedia.org/wiki/Sublime_number
Superabundant	https://en.wikipedia.org/wiki/Superabundant_number
Superior highly composite	https://en.wikipedia.org/wiki/Superior_highly_composite_number
Superperfect	https://en.wikipedia.org/wiki/Superperfect_number
Prime omega functions	https://en.wikipedia.org/wiki/Prime_omega_function
Almost prime	https://en.wikipedia.org/wiki/Almost_prime
Semiprime	https://en.wikipedia.org/wiki/Semiprime
Euler's totient function	https://en.wikipedia.org/wiki/Euler%27s_totient_function
Highly cototient	https://en.wikipedia.org/wiki/Highly_cototient_number
Highly totient	https://en.wikipedia.org/wiki/Highly_totient_number
Noncototient	https://en.wikipedia.org/wiki/Noncototient
Nontotient	https://en.wikipedia.org/wiki/Nontotient
Perfect totient	https://en.wikipedia.org/wiki/Perfect_totient_number
Sparsely totient	https://en.wikipedia.org/wiki/Sparsely_totient_number
Aliquot sequences	https://en.wikipedia.org/wiki/Aliquot_sequence
Amicable	https://en.wikipedia.org/wiki/Amicable_numbers
Perfect	https://en.wikipedia.org/wiki/Perfect_number
Sociable	https://en.wikipedia.org/wiki/Sociable_numbers
Untouchable	https://en.wikipedia.org/wiki/Untouchable_number
Primorial	https://en.wikipedia.org/wiki/Primorial
Euclid	https://en.wikipedia.org/wiki/Euclid_number
Fortunate	https://en.wikipedia.org/wiki/Fortunate_number
prime factor	https://en.wikipedia.org/wiki/Prime_factor
divisor	https://en.wikipedia.org/wiki/Divisor
Blum	https://en.wikipedia.org/wiki/Blum_integer
Cyclic	https://en.wikipedia.org/wiki/Cyclic_number_(group_theory)
Erdős–Nicolas	https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Nicolas_number
Erdős–Woods	https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Woods_number
Friendly	https://en.wikipedia.org/wiki/Friendly_number
Giuga	https://en.wikipedia.org/wiki/Giuga_number
Harmonic divisor	https://en.wikipedia.org/wiki/Harmonic_divisor_number
Jordan–Pólya	https://en.wikipedia.org/wiki/Jordan%E2%80%93P%C3%B3lya_number
Lucas–Carmichael	https://en.wikipedia.org/wiki/Lucas%E2%80%93Carmichael_number
Pronic	https://en.wikipedia.org/wiki/Pronic_number
Regular	https://en.wikipedia.org/wiki/Regular_number
Rough	https://en.wikipedia.org/wiki/Rough_number
Smooth	https://en.wikipedia.org/wiki/Smooth_number
Sphenic	https://en.wikipedia.org/wiki/Sphenic_number
Størmer	https://en.wikipedia.org/wiki/St%C3%B8rmer_number
Super-Poulet	https://en.wikipedia.org/wiki/Super-Poulet_number
Numeral system	https://en.wikipedia.org/wiki/Numeral_system
Arithmetic functions	https://en.wikipedia.org/wiki/Arithmetic_function
dynamics	https://en.wikipedia.org/wiki/Arithmetic_dynamics
Persistence	https://en.wikipedia.org/wiki/Persistence_of_a_number
Additive	https://en.wikipedia.org/wiki/Additive_persistence
Multiplicative	https://en.wikipedia.org/wiki/Multiplicative_persistence
Digit sum	https://en.wikipedia.org/wiki/Digit_sum
Digit sum	https://en.wikipedia.org/wiki/Digit_sum
Digital root	https://en.wikipedia.org/wiki/Digital_root
Self	https://en.wikipedia.org/wiki/Self_number
Sum-product	https://en.wikipedia.org/wiki/Sum-product_number
Multiplicative digital root	https://en.wikipedia.org/wiki/Multiplicative_digital_root
Sum-product	https://en.wikipedia.org/wiki/Sum-product_number
Meertens	https://en.wikipedia.org/wiki/Meertens_number
Dudeney	https://en.wikipedia.org/wiki/Dudeney_number
Factorion	https://en.wikipedia.org/wiki/Factorion
Kaprekar	https://en.wikipedia.org/wiki/Kaprekar_number
Kaprekar's constant	https://en.wikipedia.org/wiki/Kaprekar%27s_routine
Keith	https://en.wikipedia.org/wiki/Keith_number
Lychrel	https://en.wikipedia.org/wiki/Lychrel_number
Narcissistic	https://en.wikipedia.org/wiki/Narcissistic_number
Perfect digit-to-digit invariant	https://en.wikipedia.org/wiki/Perfect_digit-to-digit_invariant
Perfect digital invariant	https://en.wikipedia.org/wiki/Perfect_digital_invariant
Happy	https://en.wikipedia.org/wiki/Happy_number
P-adic numbers	https://en.wikipedia.org/wiki/P-adic_numbers
Automorphic	https://en.wikipedia.org/wiki/Automorphic_number
Trimorphic	https://en.wikipedia.org/wiki/Trimorphic_number
Digit	https://en.wikipedia.org/wiki/Numerical_digit
Palindromic	https://en.wikipedia.org/wiki/Palindromic_number
Pandigital	https://en.wikipedia.org/wiki/Pandigital_number
Repdigit	https://en.wikipedia.org/wiki/Repdigit
Repunit	https://en.wikipedia.org/wiki/Repunit
Self-descriptive	https://en.wikipedia.org/wiki/Self-descriptive_number
Smarandache–Wellin	https://en.wikipedia.org/wiki/Smarandache%E2%80%93Wellin_number
Undulating	https://en.wikipedia.org/wiki/Undulating_number
permutation	https://en.wikipedia.org/wiki/Permutation
Cyclic	https://en.wikipedia.org/wiki/Cyclic_number
Digit-reassembly	https://en.wikipedia.org/wiki/Digit-reassembly_number
Parasitic	https://en.wikipedia.org/wiki/Parasitic_number
Primeval	https://en.wikipedia.org/wiki/Primeval_number
Transposable	https://en.wikipedia.org/wiki/Transposable_integer
Equidigital	https://en.wikipedia.org/wiki/Equidigital_number
Extravagant	https://en.wikipedia.org/wiki/Extravagant_number
Frugal	https://en.wikipedia.org/wiki/Frugal_number
Harshad	https://en.wikipedia.org/wiki/Harshad_number
Polydivisible	https://en.wikipedia.org/wiki/Polydivisible_number
Smith	https://en.wikipedia.org/wiki/Smith_number
Vampire	https://en.wikipedia.org/wiki/Vampire_number
Friedman	https://en.wikipedia.org/wiki/Friedman_number
Binary numbers	https://en.wikipedia.org/wiki/Binary_number
Evil	https://en.wikipedia.org/wiki/Evil_number
Odious	https://en.wikipedia.org/wiki/Odious_number
Pernicious	https://en.wikipedia.org/wiki/Pernicious_number
sieve	https://en.wikipedia.org/wiki/Sieve_theory
Lucky	https://en.wikipedia.org/wiki/Lucky_number
Prime	https://en.wikipedia.org/wiki/Generation_of_primes
Sorting	https://en.wikipedia.org/wiki/Sorting_algorithm
Pancake number	https://en.wikipedia.org/wiki/Pancake_sorting
Sorting number	https://en.wikipedia.org/wiki/Sorting_number
Natural language	https://en.wikipedia.org/wiki/Natural_language
Aronson's sequence	https://en.wikipedia.org/wiki/Aronson%27s_sequence
Ban	https://en.wikipedia.org/wiki/Ban_number
Graphemics	https://en.wikipedia.org/wiki/Graphemics
Strobogrammatic	https://en.wikipedia.org/wiki/Strobogrammatic_number
	https://en.wikipedia.org/wiki/File:Symbol_portal_class.svg
Mathematics portal	https://en.wikipedia.org/wiki/Portal:Mathematics
https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1331878442	https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1331878442
Categories	https://en.wikipedia.org/wiki/Help:Category
Figurate numbers	https://en.wikipedia.org/wiki/Category:Figurate_numbers
Factorial and binomial topics	https://en.wikipedia.org/wiki/Category:Factorial_and_binomial_topics
Integer sequences	https://en.wikipedia.org/wiki/Category:Integer_sequences
Proof without words	https://en.wikipedia.org/wiki/Category:Proof_without_words
Squares in number theory	https://en.wikipedia.org/wiki/Category:Squares_in_number_theory
Triangles	https://en.wikipedia.org/wiki/Category:Triangles
Simplex numbers	https://en.wikipedia.org/wiki/Category:Simplex_numbers
CS1 Latin-language sources (la)	https://en.wikipedia.org/wiki/Category:CS1_Latin-language_sources_(la)
CS1 German-language sources (de)	https://en.wikipedia.org/wiki/Category:CS1_German-language_sources_(de)
Articles with short description	https://en.wikipedia.org/wiki/Category:Articles_with_short_description
Short description matches Wikidata	https://en.wikipedia.org/wiki/Category:Short_description_matches_Wikidata
Commons category link is on Wikidata	https://en.wikipedia.org/wiki/Category:Commons_category_link_is_on_Wikidata
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