A046839 Numbers k such that the number of divisors of k divides the sum of cubes of divisors of k.

1, 3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 27, 29, 30, 31, 33, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 73, 77, 78, 79, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 96, 97, 99, 101, 102, 103

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

The first 42 terms agree with A003601 but a(43) = 64 is not a term in A003601.

Examples

			64 is a term since it has 7 divisors, and sigma_3(64) = 299593 = 7 * 42799 is divisble by 7.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Crossrefs

Cf. A000005, A001158.

Cf. A003601, A020486, A046840.

Programs

Magma

[n: n in [1..110] | IsZero(DivisorSigma(3, n) mod NumberOfDivisors(n))]; // Bruno Berselli, Apr 11 2013

Mathematica

Select[Range[103], Divisible[DivisorSigma[3, #], DivisorSigma[0, #]] &] (* Jayanta Basu, Jun 29 2013 *)

PARI

isok(n) = sigma(n, 3) % numdiv(n) == 0; \\ Michel Marcus, May 13 2018