A055709 Numbers k such that k | sigma_5(k).

1, 6, 22, 28, 66, 120, 198, 264, 308, 366, 440, 604, 672, 924, 984, 1320, 1464, 1694, 1717, 2013, 2296, 2464, 2574, 2970, 3434, 3608, 3960, 4026, 4228, 4598, 4920, 5082, 5151, 5348, 6200, 6600, 6644, 6776, 6868, 6888, 7320, 7392, 8052, 8128, 9504

Offset

1,2

Comments

sigma_5(k) is the sum of the 5th powers of the divisors of k (A001160).

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..7000

Florian Luca and John Ferdinands, Problem 11090: Sometimes n divides sigma_k(n), Amer. Math. Monthly 113:4 (2006), pp. 372-373.

Mathematica

Do[If[Mod[DivisorSigma[5, n], n]==0, Print[n]], {n, 1, 15000}]
Select[Range[10000], Divisible[DivisorSigma[5, #], #]&] (* Harvey P. Dale, Aug 09 2013 *)

Prog

(PARI) is(n)=sigma(n, 5)%n==0 \\ Charles R Greathouse IV, Feb 01 2013

Crossrefs

Cf. A001160.

Cf. A055710, A055711, A055712, A055713.

Sequence in context: A242592 A044448 A111036 * A276795 A037204 A296981

Adjacent sequences: A055706 A055707 A055708 * A055710 A055711 A055712

Keyword

nonn

Author

Robert G. Wilson v, Jun 09 2000

Status

approved