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A013962
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a(n) = sigma_14(n), the sum of the 14th powers of the divisors of n.
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6
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1, 16385, 4782970, 268451841, 6103515626, 78368963450, 678223072850, 4398314962945, 22876797237931, 100006103532010, 379749833583242, 1283997101947770, 3937376385699290, 11112685048647250, 29192932133689220, 72061992352890881, 168377826559400930
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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. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001
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LINKS
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FORMULA
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Multiplicative with a(p^e) = (p^(14*e+14)-1)/(p^14-1).
Sum_{k=1..n} a(k) = zeta(15) * n^15 / 15 + O(n^16). (End)
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MATHEMATICA
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PROG
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(PARI) my(N=99, q='q+O('q^N)); Vec(sum(n=1, N, n^14*q^n/(1-q^n))) \\ Altug Alkan, Sep 10 2016
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CROSSREFS
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KEYWORD
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nonn,mult,easy
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AUTHOR
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STATUS
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approved
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