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

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Paolo P. Lava)

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(k) = 3410 and sigma_4(k) = 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. A001157, A001159, 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