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A055713 Numbers k such that k | sigma_9(k). 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

MAPLE

with(numtheory);

A055713:=proc(q)

local a, i, n;

for n from 1 to q do

  a:=divisors(n); if frac(add(a[i]^9, i=1..nops(a))/n)=0 then print(n);

fi; od; end:

A055713(100000);  # Paolo P. Lava, Dec 07 2012

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A013957.

Cf. A055709, A055710, A055711, A055712.

Sequence in context: A015492 A243843 A039293 * A216384 A352305 A060454

Adjacent sequences:  A055710 A055711 A055712 * A055714 A055715 A055716

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Jun 09 2000

STATUS

approved

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Last modified June 25 03:59 EDT 2022. Contains 354835 sequences. (Running on oeis4.)