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A055713
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Numbers k such that k | sigma_9(k).
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6
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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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.
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MAPLE
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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
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MATHEMATICA
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Do[If[Mod[DivisorSigma[9, n], n]==0, Print[n]], {n, 1, 5000}]
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PROG
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(PARI) is(n)=sigma(n, 9)%n==0 \\ Charles R Greathouse IV, Feb 04 2013
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CROSSREFS
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Cf. A013957.
Cf. A055709, A055710, A055711, A055712.
Sequence in context: A015492 A243843 A039293 * A216384 A352305 A060454
Adjacent sequences: A055710 A055711 A055712 * A055714 A055715 A055716
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v, Jun 09 2000
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STATUS
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approved
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