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 A017677 Numerator of sum of -7th powers of divisors of n. 3
 1, 129, 2188, 16513, 78126, 23521, 823544, 2113665, 4785157, 5039127, 19487172, 9032611, 62748518, 13279647, 56979896, 270549121, 410338674, 205761751, 893871740, 645047319, 1801914272, 628461297 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 FORMULA Numerators of coefficients in expansion of Sum_{k>=1} x^k/(k^7*(1 - x^k)). - Ilya Gutkovskiy, May 25 2018 EXAMPLE 1, 129/128, 2188/2187, 16513/16384, 78126/78125, 23521/23328, 823544/823543, 2113665/2097152, ... MATHEMATICA Table[Numerator[Total[Divisors[n]^-7]], {n, 30}] (* Harvey P. Dale, Nov 29 2014 *) Table[Numerator[DivisorSigma[7, n]/n^7], {n, 1, 20}] (* G. C. Greubel, Nov 07 2018 *) PROG (PARI) vector(20, n, numerator(sigma(n, 7)/n^7)) \\ G. C. Greubel, Nov 07 2018 (MAGMA) [Numerator(DivisorSigma(7, n)/n^7): n in [1..20]]; // G. C. Greubel, Nov 07 2018 CROSSREFS Cf. A017678. Sequence in context: A088719 A321563 A034681 * A013955 A294302 A221969 Adjacent sequences:  A017674 A017675 A017676 * A017678 A017679 A017680 KEYWORD nonn,frac AUTHOR STATUS approved

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Last modified January 28 03:06 EST 2020. Contains 331314 sequences. (Running on oeis4.)