A055710 Numbers k such that k | sigma_6(k).

1, 10, 26, 60, 65, 130, 150, 228, 260, 442, 650, 780, 876, 988, 1105, 1140, 1460, 1690, 1950, 2210, 2850, 2964, 3211, 3796, 4380, 4420, 4940, 5070, 5475, 5548, 6010, 6422, 8840, 9633, 10950, 11050, 11388, 11972, 12350, 12818, 13260, 13756, 14820, 16644

Offset: 1

Author

Robert G. Wilson v, Jun 09 2000

Keywords

• nonn

Comments

sigma_6(k) is the sum of the 6th powers of the divisors of k (A013954).

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 (terms 1..450 from Harvey P. Dale)
• Florian Luca and John Ferdinands, Problem 11090: Sometimes n divides sigma_k(n), Amer. Math. Monthly 113:4 (2006), pp. 372-373.

Crossrefs

Cf. A013954.

Cf. A055709, A055711, A055712, A055713.

Programs

Mathematica

Do[If[Mod[DivisorSigma[6, n], n]==0, Print[n]], {n, 1, 25000}]
Select[Range[20000],Divisible[DivisorSigma[6,#],#]&] (* Harvey P. Dale, Jun 04 2015 *)

PARI

is(n)=sigma(n,6)%n==0 \\ Charles R Greathouse IV, Feb 04 2013