A055705 Numbers k such that k | sigma_11(k) - phi(k)^11.

1, 2, 10, 12, 82, 168, 952, 1716, 2732, 2970, 5627, 8185, 11400, 12871, 20104, 20368, 23526, 25749, 70176, 82920, 111194, 117151, 119160, 128790, 134670, 143136, 185140, 193020, 208352, 240408, 247995, 251856, 291368, 354588, 565768, 592006, 642600, 783315

Offset: 1

Author

Robert G. Wilson v, Jun 09 2000

Keywords

• nonn

Comments

sigma_11(k) is the sum of the 11th powers of the divisors of k (A013959).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..124

Crossrefs

Cf. A000010, A013959.

Programs

Mathematica

Do[If[Mod[DivisorSigma[11, n]-EulerPhi[n]^11, n]==0, Print[n]], {n, 10^5}]
Select[Range[800000],Divisible[DivisorSigma[11,#]-EulerPhi[#]^11,#]&] (* Harvey P. Dale, Apr 15 2018 *)

PARI

isok(n) = !((sigma(n, 11) - eulerphi(n)^11) % n); \\ Michel Marcus, Mar 02 2014

Extensions

Definition corrected and more terms from Michel Marcus, Mar 02 2014