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%I #23 Feb 17 2024 10:32:37
%S 1,3,5,6,7,11,13,14,15,17,19,20,21,22,23,27,29,30,31,33,35,37,38,39,
%T 41,42,43,44,45,46,47,49,51,53,54,55,56,57,59,60,61,62,64,65,66,67,68,
%U 69,70,71,73,77,78,79,83,85,86,87,89,91,92,93,94,95,96,97,99,101,102,103
%N Numbers k such that the number of divisors of k divides the sum of cubes of divisors of k.
%C The first 42 terms agree with A003601 but a(43)=64 is not present in A003601.
%H T. D. Noe, <a href="/A046839/b046839.txt">Table of n, a(n) for n = 1..1000</a>
%e a(43) = 64. The sigma(k,64) values for k=0,1,2,3 are as follows: 7, 127, 5461 and 299593. While 7 does not divide the sum of divisors, 127, it divides the sum of d^3 values: Sum(d^3) = 299593 = 7*127*337.
%t Select[Range[103], Divisible[DivisorSigma[3, #], DivisorSigma[0, #]] &] (* _Jayanta Basu_, Jun 29 2013 *)
%o (Magma) [n: n in [1..110] | IsZero(DivisorSigma(3, n) mod NumberOfDivisors(n))]; // _Bruno Berselli_, Apr 11 2013
%o (PARI) isok(n) = sigma(n, 3) % numdiv(n) == 0; \\ _Michel Marcus_, May 13 2018
%Y Cf. A003601, A020486.
%K nonn
%O 1,2
%A _Labos Elemer_
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