A046871 Numbers k such that sigma(2,k) divides sigma(4,k).

1, 4, 9, 16, 20, 25, 36, 48, 49, 64, 81, 100, 121, 144, 162, 169, 180, 196, 225, 245, 256, 289, 324, 361, 400, 432, 441, 484, 500, 529, 576, 605, 625, 648, 676, 729, 784, 841, 900, 931, 961, 980, 1024, 1089, 1156, 1200, 1225, 1280, 1296, 1369, 1444, 1521

Offset

1,2

Comments

sigma_2(k) is the sum of the squares of the divisors of k (A001157).

sigma_4(k) is the sum of the 4th powers of the divisors of k (A001159).

Links

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Example

k = a(8) = 48 of which divisor power sums for powers 0,1,2,3,4 are 10, 124, 3410, 131068, 5732210, respectively. Here sigma_2 = 3410 and sigma_4 = 3410*1681.

Mathematica

Select[Range@ 1600, Divisible[DivisorSigma[4, #], DivisorSigma[2, #]] &] (* Michael De Vlieger, May 20 2017 *)

Prog

(Magma) [n: n in [1..1600] | IsZero(DivisorSigma(4, n) mod DivisorSigma(2, n))]; // Bruno Berselli, Apr 10 2013
(PARI) isok(n) = !(sigma(n, 4) % sigma(n, 2)); \\ Michel Marcus, May 21 2017

Crossrefs

Cf. A020487, A020486, A046841.

Sequence in context: A066213 A355854 A010441 * A020487 A046870 A313335

Adjacent sequences: A046868 A046869 A046870 * A046872 A046873 A046874

Keyword

nonn

Author

Labos Elemer

Status

approved