%I #66 Sep 26 2023 01:57:33
%S 1,2,3,5,6,10,15,30
%N Divisors of 30.
%C For n > 1, These are also numbers m such that k^4 + (k+1)^4 + ... + (k + m - 1)^4 is prime for some k and numbers m such that k^8 + (k+1)^8 + ... + (k + m - 1)^8 is prime for some k. - _Derek Orr_, Jun 12 2014
%C These seem to be the numbers m such that tau(n) = n*sigma(n) mod m for all n. See A098108 (mod 2), A126825 (mod 3), and A126832 (mod 5). - _Charles R Greathouse IV_, Mar 17 2022
%C The squarefree 5-smooth numbers: intersection of A051037 and A005117. - _Amiram Eldar_, Sep 26 2023
%D Boris A. Kordemsky, The Moscow Puzzles: 359 Mathematical Recreations, C. Scribner's Sons (1972), Chapter XIII, Paragraph 349.
%H Edward Barbeau and Samer Seraj, <a href="http://arxiv.org/abs/1306.5257">Sum of Cubes is Square of Sum</a>, arXiv:1306.5257 [math.NT], 2013.
%H <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>.
%F a(n) = A161715(n-1). - _Reinhard Zumkeller_, Jun 21 2009
%F Sum_{i=1..8} A000005(a(i))^3 = (Sum_{i=1..8} A000005(a(i)))^2, see Kordemsky in References and Barbeau et al. in Links section. - _Bruno Berselli_, Dec 28 2014
%e From the second comment: 1^3 + 2^3 + 2^3 + 2^3 + 4^3 + 4^3 + 4^3 + 8^3 = (1 + 2 + 2 + 2 + 4 + 4 + 4 + 8)^2 = 729. - _Bruno Berselli_, Dec 28 2014
%t Divisors[30] (* _Vladimir Joseph Stephan Orlovsky_, Dec 04 2010 *)
%o (PARI) divisors(30)
%o (Magma) Divisors(30); // _Bruno Berselli_, Dec 28 2014
%Y Cf. A000005, A005117, A051037, A158649, A161715.
%Y Cf. A098108, A126825, A126832.
%K nonn,fini,full,easy
%O 1,2
%A _N. J. A. Sloane_