A055713 Numbers k such that k | sigma_9(k).

1, 6, 38, 42, 54, 114, 120, 135, 168, 190, 216, 222, 266, 270, 280, 285, 312, 342, 378, 456, 496, 540, 570, 672, 728, 760, 798, 840, 888, 945, 1026, 1064, 1080, 1140, 1330, 1512, 1554, 1560, 1710, 1782, 1806, 1862, 1890, 1962, 1976, 1995, 1998, 2160, 2166

Offset: 1

Author

Robert G. Wilson v, Jun 09 2000

Keywords

• nonn

Comments

sigma_9(k) is the sum of the 9th powers of the divisors of k (A013957).

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. A013957.

Cf. A055709, A055710, A055711, A055712.

Programs

Mathematica

Do[If[Mod[DivisorSigma[9, n], n]==0, Print[n]], {n, 1, 5000}]

PARI

is(n)=sigma(n,9)%n==0 \\ Charles R Greathouse IV, Feb 04 2013