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==In mathematics==
==In mathematics==
'''69''', spelled '''sixty-nine''',<ref>{{cite dictionary|url=https://www.collinsdictionary.com/us/dictionary/english/sixty-nine|title=sixty-nine, n.|dictionary=[[Collins English Dictionary]]|publisher=[[HarperCollins]]|date=n.d.|access-date=22 April 2024}}</ref> is the [[natural number]] that follows [[68 (number)|68]] and precedes [[70 (number)|70]]. An [[odd number]], 69 is [[divisible]] by [[1]], [[3]] and [[23 (number)|23]] and 69.<ref>''[[A priori]]''</ref>
'''69''', spelled '''sixty-nine''', is the [[natural number]] that follows [[68 (number)|68]] and precedes [[70 (number)|70]].<ref>{{cite dictionary|url=https://www.collinsdictionary.com/us/dictionary/english/sixty-nine|title=sixty-nine, n.|dictionary=[[Collins English Dictionary]]|publisher=[[HarperCollins]]|date=n.d.|access-date=22 April 2024}}</ref><ref>{{cite web|url=https://oeis.org/A000027|title=A000027: The positive integers. Also called the natural numbers, the whole numbers or the counting numbers, but these terms are ambiguous.|last1=Neil|first1=Sloane|author1-link=Neil Sloane|last2=Forgues|first2=Daniel|date=7 October 2009|website=[[On-Line Encyclopedia of Integer Sequences]]|publisher=OEIS Foundation|access-date=22 April 2024}}</ref> An [[odd number]], 69 is [[divisible]] by [[1]], [[3]], [[23 (number)|23]] and 69.<ref>''[[A priori]]''.</ref>


69 is a [[lucky number]] and a [[composite number]], meaning that it is not a [[prime]].<ref>{{cite web|url=https://oeis.org/A000959|title=A000959: Lucky numbers|last=Neil|first=Sloane|author-link=Neil Sloane|date=7 March 2008|website=[[On-Line Encyclopedia of Integer Sequences]]|publisher=OEIS Foundation|access-date=22 April 2024}}</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}}</ref> As a natural number that is the [[product (mathematics)|product]] of exactly two prime numbers, 69 is a [[semiprime]].<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}}</ref> It is also a [[Blum integer]] since the two factors of 69 are both [[Gaussian prime]]s, and 69 is an [[interprime]] between [[67 (number)|67]] and [[71 (number)|71]].<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}}</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}}</ref> Because 69 is not divisible by any [[square number]] other than 1, it is categorised as 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}}</ref> 69 is also a [[strobogrammatic number]], because it looks the same when viewed both right-side and upside down, and a [[centered tetrahedral number]]—a centred [[figurate number]] that represents a [[tetrahedron]].<ref>{{cite book|first1=Elena|last1=Deza|first2=Michel|last2=Deza|author2-link=Michel Deza|year=2012|title=Figurative Numbers|publisher=World Scientific|isbn=9789814355483|page=127}}</ref><ref>{{cite book|first=Elena|last=Deza|author-link=Elena Deza|year=2013|title=Perfect And Amicable Numbers|publisher=[[World Scientific]]|isbn=9789811259647|page=390}}</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=63}}</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 web|url=https://www.numbersaplenty.com/69#:~:text=It%20is%20a%20cyclic%20number,It%20is%20an%20Ulam%20number.|title=69|date=n.d.|work=Numbers Aplenty|access-date=22 April 2024}}</ref>
69 is a [[composite number]], meaning that it is not a [[prime]], and a [[lucky number]].<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}}</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}}</ref> As a natural number that is the [[product (mathematics)|product]] of exactly two prime numbers (3 and 23), 69 is a [[semiprime]] and an [[interprime]] between the numbers [[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}}</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}}</ref> The [[aliquot sum]] of 69 is [[27 (number)|27]] within the aliquot sequence (69, 27, [[13 (number)|13]], 1, [[0]]) and is the third composite number in the 13-aliquot tree, following 27 and [[35 (number)|35]].{{cn|date=April 2024}} Because 69 is not divisible by any [[square number]] other than 1, it is categorised as 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}}</ref> 69 is also a [[Blum integer]] since the two factors of 69 are both [[Gaussian prime]]s, 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.<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}}</ref><ref>{{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 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>


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=63}}</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 web|url=https://www.numbersaplenty.com/69#:~:text=It%20is%20a%20cyclic%20number,It%20is%20an%20Ulam%20number.|title=69|date=n.d.|work=Numbers Aplenty|access-date=22 April 2024}}</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> Visually, 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>
It is also an [[Ulam number]],<ref>{{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> and 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 [[number theory]], 69 is 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/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}}</ref> 69 is a [[deficient number]] because the [[digit sum|sum]] of its proper divisors (excluding itself) is less than the number 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}}</ref> The [[aliquot sum]] of 69 is [[27 (number)|27]] within the aliquot sequence (69, [[27 (number)|27]], [[13 (number)|13]], [[1 (number)|1]], [[0]]) and is the third composite number in the 13-aliquot tree, following 27 and [[35 (number)|35]]. 69 is also an [[amenable number]],<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}}</ref> [[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}}</ref> [[congruent 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}}</ref> [[pernicious number]]<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> and [[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}}</ref>

In [[number theory]], 69 is a [[deficient number]] because the [[digit sum|sum]] of its proper divisors (excluding itself) is less than the number of 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}}</ref> As an integer for which the [[arithmetic mean]] average of its [[positive number|positive]] [[divisor]]s is also an integer, 69 is a [[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}}</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]] because it can be divided evenly by 2.<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}}</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}}</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}}</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}}</ref>


==In other fields==
==In other fields==

Revision as of 23:03, 22 April 2024

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

69 (sixty-nine) is the natural number following 68 and preceding 70.

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]

69 is a composite number, meaning that it is not a prime, and a lucky number.[4][5] 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.[6][7] 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.[8] 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.[9][10][11]

In decimal, 69 is the only natural number whose square (4761) and cube (328509) use every digit from 0–9 exactly once.[12] 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).[13] 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.[14] Visually, 69 is a strobogrammatic number because it looks the same when viewed both right-side and upside down.[15]

In number theory, 69 is a deficient number because the sum of its proper divisors (excluding itself) is less than the number of itself.[16] As an integer for which the arithmetic mean average of its positive divisors is also an integer, 69 is a arithmetic number.[17] 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.[18][19] 69 can be expressed as the sum of consecutive positive integers in multiple ways, making it a polite number.[20] 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.[21][22]

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).[23] In astronomy, the Messier object M69 is a globular cluster in the constellation of Sagittarius;[24] 69 Hesperia is a main-belt asteroid.[25] NGC 69 is the designation given to a barred lenticular galaxy located in the Andromeda constellation.[26][27] 69 also resembles the symbol of the zodiac sign for Cancer, ♋︎, and in the Canadian Football League, ineligible receivers wear numbers 50 to 69.[28][29]

69ing is a sex position wherein each partner aligning themselves to simultaneously achieve oral sex with each other.[30] 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".[31]

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. ^ A priori.
  4. ^ Neil, Sloane (16 December 2010). "A002808: Composite numbers". On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  5. ^ Neil, Sloane (7 March 2008). "A000959: Lucky numbers". On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  6. ^ 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.
  7. ^ Kimberling, Clark (n.d.). "A024675: Average of two consecutive odd primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  8. ^ 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.
  9. ^ Wilson, Robert G. (n.d.). "A016105: Blum integers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  10. ^ 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.
  11. ^ Deza, Elena; Deza, Michel (2012). Figurative Numbers. World Scientific. pp. 126–127. ISBN 9789814355483.
  12. ^ Wells, David (1997). The Penguin Dictionary of Curious and Interesting Numbers (2 ed.). Penguin Books. p. 63. ISBN 0-14-008029-5.
  13. ^ "69". Numbers Aplenty. n.d. Retrieved 22 April 2024.
  14. ^ Brannan, David Alexander (2006). A First Course in Mathematical Analysis. Cambridge University Press. p. 303. ISBN 9781139458955.
  15. ^ Deza, Elena (2013). Perfect And Amicable Numbers. World Scientific. p. 390. ISBN 9789811259647.
  16. ^ Sloane, Neil; Steinerberger, Stefan (31 March 2006). "A005100: Deficient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  17. ^ 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.
  18. ^ Alter, Ronald; Curtz, Thaddeus B. (January 1974). "A Note on Congruent Numbers". Mathematics of Computation. 28 (125). American Mathematical Society: 304–305.
  19. ^ Beedassy, Lekraj (7 January 2005). "A100832: Amenable numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  20. ^ 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.
  21. ^ 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.
  22. ^ 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.
  23. ^ Stwertka, Albert (2002). A Guide to the Elements (2 ed.). Oxford University Press. p. 161. ISBN 9780195150261.
  24. ^ Kitchin, C. R. (2012). Illustrated Dictionary of Practical Astronomy. Springer London. p. 262. ISBN 9781447101758.
  25. ^ 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.
  26. ^ "NGC 69". Students for the Exploration and Development of Space. n.d. Retrieved 22 April 2024.
  27. ^ 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.
  28. ^ Finey, Michele (2010). Secrets of the Zodiac: An In-Depth Guide to Your Talents, Challenges, Personality and Potential. ReadHowYouWant. p. 109. ISBN 9781458763365.
  29. ^ Higgins, Tom (7 October 2009). "An ineligible number, an eligible position". Canadian Football League. Retrieved 22 April 2024.
  30. ^ Coleman, Julia (2022). Love, Sex, and Marriage: A Historical Thesaurus. Brill Publishers. p. 214. ISBN 9789004488502.
  31. ^ Feldman, Brian (9 June 2016). "Why 69 Is the Internet's Coolest Number (Sex)". Intelligencer. Retrieved 22 April 2024.
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