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A055711 Numbers k such that k | sigma_7(k). 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

MAPLE

with(numtheory);

A055711:=proc(q)

local a, i, n;

for n from 1 to q do

  a:=divisors(n); if frac(add(a[i]^7, i=1..nops(a))/n)=0 then print(n);

fi; od; end:

A055711(100000);  # Paolo P. Lava, Dec 07 2012

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A013955.

Cf. A055709, A055710, A055712, A055713.

Sequence in context: A300906 A222198 A302650 * A141255 A091321 A125310

Adjacent sequences:  A055708 A055709 A055710 * A055712 A055713 A055714

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Jun 09 2000

STATUS

approved

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Last modified October 19 03:10 EDT 2021. Contains 348073 sequences. (Running on oeis4.)