%I #39 Jan 16 2025 19:37:07

%S 1,2,3,5,6,7,8,10,11,12,13,14,15,16,17,19,20,21,22,23,24,26,27,29,30,

%T 31,33,34,35,37,38,39,40,41,42,43,46,47,48,51,53,54,55,56,57,58,59,60,

%U 61,62,64,65,66,67,68,69,70,71,72,73,74,76,77,78,79,80,81,82,83,84,85

%N Numbers whose sum of divisors divides their sum of cubes of divisors.

%C A005117 (squarefree numbers) is a subsequence. - _Ivan Neretin_, Dec 20 2017

%H Amiram Eldar, <a href="/A046841/b046841.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Paolo P. Lava)

%e 2 is a term because 1 + 8 = 9 is divisible by 1 + 2 = 3.

%e 208 is a term: The power sums of divisors for k = 0, 1, 2, 3 are as follows: 10, 434, 54970, 10288838, and sigma(1,208) = 434 divides sigma(3,208) = 10288838 = 434*23707.

%p with(numtheory):

%p for n to 100 do

%p if (type(sigma[3](n)/sigma[1](n), integer)) then print(n) end if;

%p end do; # _Peter Bala_, Jan 12 2025

%t Select[Range@ 85, Divisible[DivisorSigma[3, #], DivisorSigma[1, #]] &] (* _Michael De Vlieger_, Aug 01 2017 *)

%o (PARI) isA046841(n)=sigma(n,3)%sigma(n,1)==0 \\ _Michael B. Porter_, Apr 07 2010

%Y Cf. A000203, A001158, A005117.

%Y Cf. A003601, A020486.

%K nonn,changed

%O 1,2

%A _Labos Elemer_