A055711 Numbers k such that k | sigma_7(k).

1, 6, 28, 86, 120, 145, 258, 290, 435, 496, 580, 588, 672, 696, 870, 946, 1032, 1305, 1720, 1740, 2245, 2610, 2712, 2838, 3164, 3282, 3408, 3480, 3724, 3784, 4060, 4490, 5160, 5220, 6735, 6786, 6960, 7830, 8514, 8980, 9436, 9492, 9632, 9976

Offset: 1

Author

Robert G. Wilson v, Jun 09 2000

Keywords

• nonn

Comments

sigma_7(k) is the sum of the 7th powers of the divisors of k (A013955).

Problem 11090 proves that this sequence is infinite. - T. D. Noe, Apr 18 2006

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Florian Luca and John Ferdinands, Problem 11090: Sometimes n divides sigma_k(n), Amer. Math. Monthly 113:4 (2006), pp. 372-373.

Crossrefs

Cf. A013955.

Cf. A055709, A055710, A055712, A055713.

Programs

Mathematica

Do[If[Mod[DivisorSigma[7, n], n]==0, Print[n]], {n, 1, 10000}]

PARI

is(n)=sigma(n,7)%n==0 \\ Charles R Greathouse IV, Feb 04 2013