View source for 69 (number)

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{{Infobox number
| number = 69
| divisor = 1, 3, 23, 69
|lang1=[[Chinese numeral]],<br/>[[Japanese numeral]]
|lang1 symbol=六十九
|lang2=[[ASCII|ASCII value]]
|lang2 symbol=[[E]]
}}
'''69''' ('''sixty-nine''') is the [[natural number]] following [[68 (number)|68]] and preceding [[70 (number)|70]]. An [[odd number]] and a [[composite number]], 69 is [[divisible]] by [[1]], [[3]], [[23 (number)|23]] and 69.

The number and its pictograph give its name to the [[sexual position]] of [[69ing|the same name]]. The association of the number with this sex position has resulted in it being associated in [[internet meme|meme culture]] with sex.

==In mathematics==
69 is a [[semiprime]] because it is a natural number that is the [[product (mathematics)|product]] of exactly two prime numbers (3 and 23), and it is an [[interprime]] between the numbers of [[67 (number)|67]] and [[71 (number)|71]].<ref>{{cite web|url=https://oeis.org/A001358|title=A001358: Semiprimes (or biprimes): products of two primes.|last1=Neil|first1=Sloane|last2=Guy|first2=R. K.|author2-link=Richard K. Guy|date=22 August 2010|website=On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=22 April 2024|archive-date=19 April 2019|archive-url=https://web.archive.org/web/20190419095507/https://oeis.org/A001358|url-status=live}}</ref><ref>{{cite web|url=https://oeis.org/A024675|first=Clark|last=Kimberling|author-link=Clark Kimberling|date=n.d.|title=A024675: Average of two consecutive odd primes.|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=22 April 2024|archive-date=4 March 2024|archive-url=https://web.archive.org/web/20240304232723/https://oeis.org/A024675|url-status=live}}</ref> 69 is not divisible by any [[square number]] other than 1, making it a [[square-free integer]].<ref>{{cite web|url=https://oeis.org/A005117|first=Neil|last=Sloane|date=n.d.|title=A005117: Squarefree numbers: numbers that are not divisible by a square greater than 1.|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=22 April 2024|archive-date=27 May 2019|archive-url=https://web.archive.org/web/20190527172638/http://oeis.org/A005117|url-status=live}}</ref> 69 is a [[Blum integer]] since the two factors of 69 are both [[Gaussian prime]]s, and an [[Ulam number]]—an integer that is the sum of two distinct previously occurring Ulam numbers in a sequence.{{efn|As a consequence of the definition of the Ulam sequence, 3 is an Ulam number (1 + 2) and 4 is an Ulam number (1 + 3). 5 is not an Ulam number, because 5 <nowiki>=</nowiki> 1 + 4 <nowiki>=</nowiki> 2 + 3. 69 is an Ulam number as the sum of 16 + 53; both 16 and 53 are Ulam numbers.<ref name="Gupta">{{cite book|first=Shyam Sunder|last=Gupta|editor-last=Wenpeng|editor-first=Zhang|year=2009|chapter=Smarandache sequence of Ulam numbers|title=Research on Number Theory and Smarandache Notions: Proceedings of the Fifth International Conference on Number Theory and Smarandache Notions|publisher=Hexis|isbn=9781599730882|page=78}}</ref><ref>{{cite journal|last=Recaman|first=Bernardo|year=1973|title=Questions on a sequence of Ulam|journal=[[American Mathematical Monthly]]|publisher=[[Mathematical Association of America]]|issue=8|volume=80|pages=919–920|doi=10.2307/2319404|jstor=2319404 }}</ref>}}<ref name="Gupta"/><ref>{{cite web|url=https://oeis.org/A016105|first=Robert G.|last=Wilson|date=n.d.|title=A016105: Blum integers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=22 April 2024|archive-date=17 October 2018|archive-url=https://web.archive.org/web/20181017021517/http://oeis.org/A016105|url-status=live}}</ref> 69 is a [[deficient number]] because the [[Aliquot sum|sum of its proper divisors]] (which excludes itself) is less than itself.<ref>{{cite web|url=https://oeis.org/A005100|first1=Neil|last1=Sloane|first2=Stefan|last2=Steinerberger|date=31 March 2006|title=A005100: Deficient numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=22 April 2024|archive-date=22 March 2023|archive-url=https://web.archive.org/web/20230322182824/https://oeis.org/A005100|url-status=live}}</ref> As an integer for which the [[arithmetic mean]] average of its [[positive number|positive]] [[divisor]]s is also an integer, 69 is an [[arithmetic number]].<ref>{{cite web|url=https://oeis.org/A003601|last1=Sloane|first1=Neil|last2=Bernstein|first2=Mira|date=3 April 2006|title=A003601: Numbers j such that the average of the divisors of j is an integer: sigma_0(j) divides sigma_1(j). Alternatively, numbers j such that tau(j) (A000005(j)) divides sigma(j) (A000203(j)).|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=22 April 2024|archive-date=26 March 2024|archive-url=https://web.archive.org/web/20240326083848/https://oeis.org/A003601|url-status=live}}</ref> 69 is a [[congruent number]]—a positive integer that is the area of a [[right triangle]] with three [[rational number]] sides—and an [[amenable number]].<ref>{{cite journal|first1=Ronald|last1=Alter|first2=Thaddeus B.|last2=Curtz|date=January 1974|title=A Note on Congruent Numbers|journal=[[Mathematics of Computation]]|publisher=[[American Mathematical Society]]|volume=28|number=125|pages=304–305|doi=10.2307/2005838|jstor=2005838}}</ref><ref>{{cite web|url=https://oeis.org/A100832|last=Beedassy|first=Lekraj|date=7 January 2005|title=A100832: Amenable numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=22 April 2024|archive-date=19 December 2023|archive-url=https://web.archive.org/web/20231219114919/https://oeis.org/A100832|url-status=live}}</ref> 69 can be expressed as the sum of consecutive positive integers in multiple ways, making it a [[polite number]].<ref>{{cite web|url=https://oeis.org/A138591|first1=Vladimir Joseph Stephan|last1=Orlovsky|first2=Carl R.|last2=White|date=22 July 2009|title=A138591: Sums of two or more consecutive nonnegative integers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=22 April 2024|archive-date=12 March 2019|archive-url=https://web.archive.org/web/20190312031016/http://oeis.org/A138591|url-status=live}}</ref> 69 is a [[lucky number]] because it is a natural number that remains after repeatedly removing every ''n''th number in a sequence of natural numbers, starting from 1.{{efn|Where ''n'' is the next number in the list after the last surviving number; every second number (all [[even number]]s) in the list of numbers (1 through [[infinity]]) is eliminated first (1, 3, 5, 7, 9, 11 …), every third number (1, 3, 7, 9 …), then every seventh number, and so forth.<ref>{{cite book|last=Giblin|first=P[eter] J.|author-link=Peter Giblin|year=1993|title=Primes and Programming|publisher=[[Cambridge University Press]]|isbn=9780521409889|page=67}}</ref>}}<ref>{{cite web|url=https://oeis.org/A002808|title=A002808: Composite numbers|last=Neil|first=Sloane|date=16 December 2010|website=On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=22 April 2024|archive-date=11 May 2024|archive-url=https://web.archive.org/web/20240511171822/https://oeis.org/A002808|url-status=live}}</ref><ref>{{cite web|url=https://oeis.org/A000959|title=A000959: Lucky numbers|last=Neil|first=Sloane|date=7 March 2008|website=On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=22 April 2024|archive-date=19 April 2019|archive-url=https://web.archive.org/web/20190419095457/https://oeis.org/A000959|url-status=live}}</ref>

In [[decimal]], 69 is the only natural number whose [[square (algebra)|square]] ({{val|4761}}) and [[cube (algebra)|cube]] ({{val|328509}}) use every digit from 0–9 exactly once.<ref>{{cite book|last=Wells|first=David|year=1997|title=[[The Penguin Dictionary of Curious and Interesting Numbers]]|edition=2|publisher=[[Penguin Books]]|isbn=0-14-008029-5|page=100}}</ref><ref>{{cite book|last=Barbeau|first=Edward|author-link=Edward Barbeau|year=1997|title=Power Play|publisher=Mathematical Association of America|isbn=9780883855232|page=126}}</ref> It is also the largest number whose [[factorial]] is less than a [[googol]]. On many handheld scientific and graphing [[calculator]]s, 69! (1.711224524{{e|98}}) is the highest factorial that can be calculated due to memory limitations.<ref>{{cite book|first=David Alexander|last=Brannan|year=2006|title=A First Course in Mathematical Analysis|publisher=[[Cambridge University Press]]|isbn=9781139458955|page=303}}</ref> In its [[binary number|binary expansion]] of 1000101,<ref>{{cite book|last=Konheim|first=Alan G.|year=2007|title=Computer Security and Cryptography|publisher=Wiley|isbn=9780470083970|page=382}}</ref> 69 is equal to [[105 (number)|105]] [[octal]], while 105 is equal to 69 [[hexadecimal]] (this same property can be applied to all numbers from [[64 (number)|64]] to 69).<ref>{{cite book|last=Topham|first=Douglas W.|year=2012|title=A System V Guide to UNIX and XENIX|publisher=[[Springer New York]]|isbn=9781461232469|page=78}}</ref><ref name="Holmay">{{cite book|last=Holmay|first=Patrick|year=1998|chapter=ASCII Character Set (Continued)|title=The OpenVMS User's Guide|publisher=[[Elsevier Science]]|isbn=9781555582036|page=272}}</ref> In [[computing]], 69 equates to 2120 in [[base 3|ternary]] (base-3); 153 in [[senary]] (base-6); and 59 in [[duodecimal]] (base-12).<ref>{{cite book|last1=Clifford|first1=Jerrold R.|last2=Clifford|first2=Martin|year=1974|title=Computer Mathematics Handbook|publisher=[[Allyn & Bacon]]|page=276}}</ref><ref>{{cite book|last=Scott|first=Norman Ross|year=1960|title=Analog and Digital Computer Technology|publisher=[[McGraw-Hill]]|page=221}}</ref><ref>{{cite book|last=Meyer|first=Jerome S.|year=1963|title=More Fun with Mathematics|publisher=[[Gramercy Publishing Company]]|page=73}}</ref>

Visually, in [[Arabic numerals]], 69 is a [[strobogrammatic number]] because it looks the same when viewed both right-side and upside down.<ref>{{cite book|first=Elena|last=Deza|year=2013|title=Perfect And Amicable Numbers|publisher=World Scientific|isbn=9789811259647|page=390}}</ref> 69 is a [[centered tetrahedral number]], a [[figurate number]] that represents a [[Pyramid (geometry)|pyramid]] with a triangular base and all other points arranged in layers above the base, forming a [[tetrahedron]] shape.<ref>{{cite book|first1=Elena|last1=Deza|first2=Michel|last2=Deza|author1-link=Elena Deza|author2-link=Michel Deza|year=2012|title=Figurative Numbers|publisher=[[World Scientific]]|isbn=9789814355483|pages=126–127}}</ref> 69 is also a [[pernicious number]] because there is a prime number of 1s when it is written as a [[binary number]], and an [[odious number]] as it is a positive integer that has an odd number of 1s in its binary expansion.<ref>{{cite web|url=https://oeis.org/A052294|last=Gow|first=Jeremy|date=8 February 2000|title=A052294: Pernicious numbers: numbers with a prime number of 1's in their binary expansion|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=22 April 2024}}</ref><ref>{{cite web|url=https://oeis.org/A000069|first=Neil|last=Sloane|date=n.d.|title=A000069: Odious numbers: numbers with an odd number of 1's in their binary expansion|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=22 April 2024|archive-date=11 September 2018|archive-url=https://web.archive.org/web/20180911114600/https://oeis.org/A000069|url-status=live}}</ref>

==In culture==
[[69ing]] is a [[sex position]] wherein each partner aligns themselves to simultaneously achieve [[oral sex]] with each other.<ref>{{cite book|last=Coleman|first=Julia|year=2022|title=Love, Sex, and Marriage: A Historical Thesaurus|publisher=[[Brill Publishers]]|isbn=9789004488502|page=214}}</ref> In reference to this sex act, the number 69 itself has become an [[Internet meme]] as an inherently funny number in which users will respond to any occurrence of the number with the word "nice" to draw specific attention to it.<ref name="dyk"/> This means to humorously imply that the reference to the sex position was intentional. Because of its association with the sex position and resulting meme, 69 has been named "the sex number".<ref name="dyk">{{cite news|last=Feldman|first=Brian|date=9 June 2016|title=Why 69 Is the Internet's Coolest Number (Sex)|publisher=[[Intelligencer (website)|Intelligencer]]|url=https://nymag.com/intelligencer/2016/06/why-69-is-the-internets-coolest-number-sex.html|access-date=22 April 2024|archive-date=4 August 2022|archive-url=https://web.archive.org/web/20220804212814/https://nymag.com/intelligencer/2016/06/why-69-is-the-internets-coolest-number-sex.html|url-status=live}}</ref>

On American highways, "69 mile" marker signs are frequently [[Street sign theft|stolen]]. As a result, the [[Colorado Department of Transportation|Colorado DOT]] began replacing them with "68.5 mile" ones.<ref>{{cite news|url=https://www.denverpost.com/2014/01/10/colorado-hopes-a-mile-419-99-sign-on-interstate-70-thwarts-stoners/|title=Colorado hopes a Mile 419.99 sign on Interstate 70 thwarts stoners|first=John|last=Ingold|publisher=[[The Denver Post]]|date=2 October 2016|access-date=1 June 2025}}</ref><ref>{{cite news|url=http://mentalfloss.com/article/67576/stoners-keep-stealing-420-mile-markers-so-some-states-have-replaced-them-4199|title=Stoners Keep Stealing 420 Mile Markers, So Some States Have Replaced Them With 419.9|first=Hannah|last=Keyser|publisher=[[Mental Floss]]|date=20 August 2015|access-date=1 June 2025}}</ref>

==See also==
*[[6-7 (meme)]] – Internet meme
*[[96 (number)]] – 69 reversed
*[[420 (cannabis culture)]] – another slang term that has also led to [[street sign theft]]

==Explanatory footnotes==
{{notelist}}

==References==
{{reflist}}

{{Integers|zero}}

{{DEFAULTSORT:69 (Number)}}
[[Category:Integers]]
[[Category:Internet memes]]
[[Category:Numerical memes]]