Wikipedia

69 (number)

69 (sixty-nine) is the natural number following 68 and preceding 70. An odd number and a composite number, 69 is divisible by 1, 3, 23 and 69. 69 is a semiprime because it is a natural number that is the product of exactly two prime numbers (3 and 23), and an interprime between the numbers of 67 and 71. Because 69 is not divisible by any square number other than 1, it is categorised as a square-free integer. 69 is also a Blum integer since the two factors of 69 are both Gaussian primes. In number theory, 69 is a deficient number, arithmetic number and a congruent number.

← 68 69 70 →
Cardinalsixty-nine
Ordinal69th
(sixty-ninth)
Factorization3 × 23
Divisors1, 3, 23, 69
Greek numeralΞΘ´
Roman numeralLXIX
Binary10001012
Ternary21203
Senary1536
Octal1058
Duodecimal5912
Hexadecimal4516

In reference to 69ing, a sex position in which two partners align themselves to simultaneously achieve oral sex, 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. Because of its association with the sex position and resulting meme, 69 has been humorously named "the sex number".

In mathematics

69, spelled sixty-nine, is the natural number that follows 68 and precedes 70.[1][2] An odd number, 69 is divisible by 1, 3, 23 and 69.[3][4]

69 is a composite number, meaning that it is not a prime, and a lucky number.[5][6] As a natural number that is the product of exactly two prime numbers (3 and 23), 69 is a semiprime and an interprime between the numbers 67 and 71.[7][8] The aliquot sum of 69 is 27 within the aliquot sequence (69, 27, 13, 1, 0) and is the third composite number in the 13-aliquot tree, following 27 and 35.[citation needed] Because 69 is not divisible by any square number other than 1, it is categorised as a square-free integer.[9] 69 is also a Blum integer since the two factors of 69 are both Gaussian primes, an Ulam number, and a centered tetrahedral number—a figurate number that represents a pyramid with a triangular base and all other points arranged in layers above the base, forming a tetrahedron shape.[10][11][12]

In decimal, 69 is the only natural number whose square (4761) and cube (328509) use every digit from 0–9 exactly once.[13] 69 is equal to 105 octal, while 105 is equal to 69 hexadecimal (this same property can be applied to all numbers from 64 to 69).[14] It is also the largest number whose factorial is less than a googol. On many handheld scientific and graphing calculators, 69! (1.711224524×1098) is the highest factorial that can be calculated due to memory limitations.[15] Visually, 69 is a strobogrammatic number because it looks the same when viewed both right-side and upside down.[16]

In number theory, 69 is a deficient number because the sum of its proper divisors (excluding itself) is less than the number of itself.[17] As an integer for which the arithmetic mean average of its positive divisors is also an integer, 69 is a arithmetic number.[18] 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 because it can be divided evenly by 2.[19][20] 69 can be expressed as the sum of consecutive positive integers in multiple ways, making it a polite number.[21] 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.[22][23]

In other fields

See also: list of highways numbered 69

In chemistry, 69 is the atomic number of thulium, a rare lanthanide (category of metallic elements).[24] In astronomy, the Messier object M69 is a globular cluster in the constellation of Sagittarius;[25] 69 Hesperia is a main-belt asteroid.[26] NGC 69 is the designation given to a barred lenticular galaxy located in the Andromeda constellation.[27][28] 69 also resembles the symbol for the zodiac sign for Cancer, ♋︎, and in the Canadian Football League, ineligible receivers wear numbers 50 to 69.[29][30] In ASCII, 69 is the decimal for the uppercase E character.[31]

69ing is a sex position wherein each partner aligning themselves to simultaneously achieve oral sex with each other.[32] 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. 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".[33] In music, the American rapper 6ix9ine (pronounced "six nine") chose the stage name in reference to the sex position as well as the yin-yang symbol.[34]

See also

References

  1. ^ "sixty-nine, n.". Collins English Dictionary. HarperCollins. n.d. Retrieved 22 April 2024.
  2. ^ Neil, Sloane; Forgues, Daniel (7 October 2009). "A000027: The positive integers. Also called the natural numbers, the whole numbers or the counting numbers, but these terms are ambiguous". On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  3. ^ Neil, Sloane (9 May 2022). "A005408: The odd numbers". On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 23 April 2024.
  4. ^ Anjema, Henry (1767). Table of divisors of all the natural numbers from 1. to 10000. p. 2. ISBN 9781140919421 – via the Internet Archive.
  5. ^ Neil, Sloane (16 December 2010). "A002808: Composite numbers". On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  6. ^ Neil, Sloane (7 March 2008). "A000959: Lucky numbers". On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  7. ^ Neil, Sloane; Guy, R. K. (22 August 2010). "A001358: Semiprimes (or biprimes): products of two primes". On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  8. ^ Kimberling, Clark (n.d.). "A024675: Average of two consecutive odd primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  9. ^ Sloane, Neil (n.d.). "A005117: Squarefree numbers: numbers that are not divisible by a square greater than 1". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  10. ^ Wilson, Robert G. (n.d.). "A016105: Blum integers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  11. ^ Gupta, Shyam Sunder (2009). "Smarandache sequence of Ulam numbers". In Wenpeng, Zhang (ed.). Research on Number Theory and Smarandache Notions: Proceedings of the Fifth International Conference on Number Theory and Smarandache Notions. Hexis. p. 78. ISBN 9781599730882.
  12. ^ Deza, Elena; Deza, Michel (2012). Figurative Numbers. World Scientific. pp. 126–127. ISBN 9789814355483.
  13. ^ Wells, David (1997). The Penguin Dictionary of Curious and Interesting Numbers (2 ed.). Penguin Books. p. 63. ISBN 0-14-008029-5.
  14. ^ "69". Numbers Aplenty. n.d. Retrieved 22 April 2024.
  15. ^ Brannan, David Alexander (2006). A First Course in Mathematical Analysis. Cambridge University Press. p. 303. ISBN 9781139458955.
  16. ^ Deza, Elena (2013). Perfect And Amicable Numbers. World Scientific. p. 390. ISBN 9789811259647.
  17. ^ Sloane, Neil; Steinerberger, Stefan (31 March 2006). "A005100: Deficient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  18. ^ Sloane, Neil; Bernstein, Mira (3 April 2006). "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))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  19. ^ Alter, Ronald; Curtz, Thaddeus B. (January 1974). "A Note on Congruent Numbers". Mathematics of Computation. 28 (125). American Mathematical Society: 304–305.
  20. ^ Beedassy, Lekraj (7 January 2005). "A100832: Amenable numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  21. ^ Orlovsky, Vladimir Joseph Stephan; White, Carl R. (22 July 2009). "A138591: Sums of two or more consecutive nonnegative integers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  22. ^ Gow, Jeremy (8 February 2000). "A052294: Pernicious numbers: numbers with a prime number of 1's in their binary expansion". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  23. ^ Sloane, Neil (n.d.). "A000069: Odious numbers: numbers with an odd number of 1's in their binary expansion". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  24. ^ Stwertka, Albert (2002). A Guide to the Elements (2 ed.). Oxford University Press. p. 161. ISBN 9780195150261.
  25. ^ Kitchin, C. R. (2012). Illustrated Dictionary of Practical Astronomy. Springer London. p. 262. ISBN 9781447101758.
  26. ^ Shepard, Michael K.; Harris, Alan W.; Taylor, Patrick A.; Clark, Beth Ellen; Ockert-Bell, Maureen; Nolan, Michael C.; et al. (3 August 2011). "Radar observations of Asteroids 64 Angelina and 69 Hesperia" (PDF). Icarus. 215 (2). Elsevier: 547–551. Retrieved 22 April 2024 – via NASA.
  27. ^ "NGC 69". Students for the Exploration and Development of Space. n.d. Retrieved 22 April 2024.
  28. ^ Steinicke, Wolfgang (2010). Observing and Cataloguing Nebulae and Star Clusters: From Herschel to Dreyer's New General Catalogue. Cambridge University Press. p. 191. ISBN 9781139490108.
  29. ^ Finey, Michele (2010). Secrets of the Zodiac: An In-Depth Guide to Your Talents, Challenges, Personality and Potential. ReadHowYouWant. p. 109. ISBN 9781458763365.
  30. ^ Higgins, Tom (7 October 2009). "An ineligible number, an eligible position". Canadian Football League. Retrieved 22 April 2024.
  31. ^ "ASCII printable characters". American Standard Code for Information Interchange. n.d. Retrieved 23 April 2024.
  32. ^ Coleman, Julia (2022). Love, Sex, and Marriage: A Historical Thesaurus. Brill Publishers. p. 214. ISBN 9789004488502.
  33. ^ Feldman, Brian (9 June 2016). "Why 69 Is the Internet's Coolest Number (Sex)". Intelligencer. Retrieved 22 April 2024.
  34. ^ Witt, Stephen (16 January 2019). "Tekashi 69: The Rise and Fall of a Hip-Hop Supervillain". Rolling Stone. Retrieved 23 April 2024.
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