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A013956
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sigma_8(n), the sum of the 8th powers of the divisors of n.
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4
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1, 257, 6562, 65793, 390626, 1686434, 5764802, 16843009, 43053283, 100390882, 214358882, 431733666, 815730722, 1481554114, 2563287812, 4311810305, 6975757442, 11064693731, 16983563042, 25700456418
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OFFSET
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1,2
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COMMENTS
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If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1).
Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - comment from Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001.
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LINKS
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Table of n, a(n) for n=1..20.
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FORMULA
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G.f. sum(k>=1, k^8*x^k/(1-x^k)). - Benoit Cloitre, Apr 21 2003
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MATHEMATICA
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lst={}; Do[AppendTo[lst, DivisorSigma[8, n]], {n, 5!}]; lst [From Vladimir Joseph Stephan Orlovsky, Mar 11 2009]
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PROG
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(Sage) [sigma(n, 8)for n in xrange(1, 21)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 04 2009]
(PARI) a(n)=sigma(n, 8) \\ Charles R Greathouse IV, Apr 28, 2011
(MAGMA) [DivisorSigma(8, n): n in [1..30]]; // Bruno Berselli, Apr 10 2013
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CROSSREFS
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Sequence in context: A155468 A034682 A017679 * A036086 A000542 A023877
Adjacent sequences: A013953 A013954 A013955 * A013957 A013958 A013959
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KEYWORD
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nonn,mult,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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