A055712 Numbers k such that k | sigma_8(k).

1, 84, 156, 204, 364, 476, 514, 1092, 1428, 2316, 2652, 2892, 6069, 6188, 6748, 12138, 12532, 16212, 16388, 18564, 20244, 24276, 30108, 37596, 39372, 49164, 63291, 78897, 87724, 99202, 114716, 126582, 147679, 157794, 167331

Offset: 1

Author

Robert G. Wilson v, Jun 09 2000

Keywords

• nonn

Comments

sigma_8(k) is the sum of the 8th powers of the divisors of k (A013956).

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..1000
• Florian Luca and John Ferdinands, Problem 11090: Sometimes n divides sigma_k(n), Amer. Math. Monthly 113:4 (2006), pp. 372-373.

Crossrefs

Cf. A013956.

Cf. A055709, A055710, A055711, A055713.

Programs

Mathematica

Do[If[Mod[DivisorSigma[8, n], n]==0, Print[n]], {n, 1, 10000}]
Select[Range[170000],Divisible[DivisorSigma[8,#],#]&] (* Harvey P. Dale, Sep 15 2019 *)

PARI

is(n)=sigma(n,8)%n==0 \\ Charles R Greathouse IV, Feb 04 2013