A067313 Numbers k such that sigma_k(k)/k is an integer, where sigma_k(k) is the sum of the k-th powers of the divisors of k (A023887).

1, 10, 130, 135, 147, 150, 228, 250, 350, 364, 410, 444, 492, 876, 891, 945, 1014, 1308, 1372, 1550, 1690, 1950, 2050, 2210, 2373, 2565, 2850, 3045, 3050, 3250, 3375, 3876, 4108, 4185, 4905, 4995, 5050, 5070, 5145, 5330, 5439, 5481, 6150, 6250, 6321, 6615, 6890, 7514

Offset

1,2

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Amiram Eldar)

Example

If k = 10, then sigma(10,10) = 1 + 1024 + 9765625 + 10000000000 = 1009766650 is divisible by k = 10.

Mathematica

Do[s=DivisorSigma[n, n]; If[IntegerQ[s/n], Print[n]], {n, 1, 10000}]
Select[Range[6500], Divisible[DivisorSigma[#, #], #]&] (* Harvey P. Dale, Feb 06 2019 *)

Prog

(PARI) isok(k) = !(sigma(k, k) % k); \\ Michel Marcus, Aug 10 2020
(PARI) is(n) = {my(d = divisors(n), v = vecsum(vector(#d - 1, i, Mod(d[i], n)^n))); lift(v)==0} \\ David A. Corneth, Aug 10 2020

Crossrefs

Cf. A023887.

Sequence in context: A360941 A007819 A054050 * A104130 A327810 A355422

Adjacent sequences: A067310 A067311 A067312 * A067314 A067315 A067316

Keyword

nonn

Author

Labos Elemer, Jan 14 2002

Status

approved