A046840 Numbers k such that the number of divisors of k divides the sum of the 4th powers of the divisors of k.

1, 3, 4, 5, 7, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 25, 27, 28, 29, 31, 33, 35, 37, 39, 41, 43, 44, 47, 48, 49, 51, 52, 53, 55, 57, 59, 60, 61, 65, 67, 68, 69, 71, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 89, 91, 92, 93, 95, 97, 100, 101, 103, 105, 107, 108, 109, 111

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

A020486 is very similar to this sequence, but it does not include the following values below 1000 (which this sequence does include): {16, 80, 81, 176, 304, 324, 400, 405, 464, 496, 656, 784, 880, 891, 944, 976}.

Examples

			k = 16 is a term since it has 5 divisors, and sigma_4(16) = 69905 is divisible by 5.
		

Links

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

Crossrefs

Cf. A000005, A001159.

Cf. A003601, A020486, A046839.

Programs

Magma

[n: n in [1..120] | IsZero(DivisorSigma(4, n) mod NumberOfDivisors(n))]; // Bruno Berselli, Apr 11 2013

Mathematica

Select[Range[120], Divisible[DivisorSigma[4, #], DivisorSigma[0, #]] &] (* Amiram Eldar, Mar 17 2025 *)

PARI

isok(n) = sigma(n, 4) % numdiv(n) == 0; \\ Michel Marcus, May 13 2018