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A017691
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Numerator of sum of -14th powers of divisors of n.
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3
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1, 16385, 4782970, 268451841, 6103515626, 39184481725, 678223072850, 4398314962945, 22876797237931, 10000610353201, 379749833583242, 213999516991295, 3937376385699290, 5556342524323625, 5838586426737844, 72061992352890881, 168377826559400930, 374836322743499435
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OFFSET
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1,2
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COMMENTS
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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. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001
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LINKS
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FORMULA
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Dirichlet g.f. of a(n)/A017692(n): zeta(s)*zeta(s+14).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A017692(k) = zeta(15) (A013673). (End)
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MATHEMATICA
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Table[Numerator[DivisorSigma[14, n]/n^14], {n, 1, 20}] (* G. C. Greubel, Nov 06 2018 *)
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PROG
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(PARI) vector(20, n, numerator(sigma(n, 14)/n^14)) \\ G. C. Greubel, Nov 06 2018
(Magma) [Numerator(DivisorSigma(14, n)/n^14): n in [1..20]]; // G. C. Greubel, Nov 06 2018
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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