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A018253
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Divisors of 24.
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43
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OFFSET
| 1,2
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COMMENTS
| The divisors of 24 greater than 1 are the only positive integers n with the property m^2 == 1 (mod n) for all integer m coprime to n. - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 10 2001
n for which all Dirichlet characters are real. - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 21 2002
These are the numbers n that are divisible by all numbers less than or equal to square root of n. - Tanya Khovanova (tanyakh(AT)yahoo.com), Dec 10 2006
Also, numbers n such that A160812(n) = 0. - Omar E. Pol (info(AT)polprimos.com), Jun 19 2009
It appears that these are the only positive integers n such that A160812(n) = 0. [From Omar E. Pol (info(AT)polprimos.com), Nov 17 2009]
24 is a highly composite number: A002182(6)=24. [From Reinhard Zumkeller, Jun 21 2010]
Chebolu points out that these are exactly the numbers for which the multiplication table of the integers mod n have 1s only on their diagonal, i.e., ab = 1 (mod n) implies a = b (mod n). [Charles R Greathouse IV, Jul 06 2011]
It appears that 3, 4, 6, 8, 12, 24 (the divisors >= 3 of 24) are also the only numbers n whose proper non-divisors k are prime numbers if k = d-1 and d divides n. - Omar E. Pol, Sep 23 2011
About the last Pol's comment: I have searched to 10^7 and have found no other terms. - Robert G. Wilson, Sep 23 2011.
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REFERENCES
| Harvey Cohn, "Advanced Number Theory", Dover, chap.II, p. 38
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LINKS
| Index entries for sequences related to divisors of numbers
M. H. Eggar, A curious property of the integer 24, Math. Gazette 84 (2000), pp. 96-97.
Sunil K. Chebolu, What is special about the divisors of 24?, 2011
Eric Weisstein's World of Mathematics, Modulo Multiplication Group
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FORMULA
| a(n) = A161710(n-1). [From Reinhard Zumkeller, Jun 21 2009]
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MATHEMATICA
| Divisors[24] (* From Vladimir Joseph Stephan Orlovsky, Feb 16 2012 *)
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PROG
| (Sage) divisors(24); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 13 2009]
(PARI) divisors(24) \\ Charles R Greathouse IV, Apr 28, 2011
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CROSSREFS
| Cf. A174228. [From Reinhard Zumkeller, May 24 2010]
Cf. A018256, A018261, A018266, A018293, A018321, A018350, A018412, A018609, A018676, A178877, A178878, A165412, A178858, A178859, A178860, A178861, A178862, A178863, A178864. [From Reinhard Zumkeller, Jun 21 2010]
Sequence in context: A007886 A135108 A018515 * A143417 A018597 A018623
Adjacent sequences: A018250 A018251 A018252 * A018254 A018255 A018256
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KEYWORD
| nonn,fini,full,easy,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com)
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