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 A017678 Denominator of sum of -7th powers of divisors of n. 3
 1, 128, 2187, 16384, 78125, 23328, 823543, 2097152, 4782969, 5000000, 19487171, 8957952, 62748517, 13176688, 56953125, 268435456, 410338673, 204073344, 893871739, 640000000, 1801088541, 623589472 (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 Vincenzo Librandi, Table of n, a(n) for n = 1..1000 FORMULA Denominators 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[Denominator[Total[Divisors[n]^-7]], {n, 30}] (* Harvey P. Dale, Mar 21 2012 *) Table[Denominator[DivisorSigma[7, n]/n^7], {n, 1, 20}] (* G. C. Greubel, Nov 07 2018 *) PROG (PARI) vector(20, n, denominator(sigma(n, 7)/n^7)) \\ G. C. Greubel, Nov 07 2018 (Magma) [Denominator(DivisorSigma(7, n)/n^7): n in [1..20]]; // G. C. Greubel, Nov 07 2018 CROSSREFS Cf. A017677. Sequence in context: A224138 A331198 A250365 * A123253 A001015 A352053 Adjacent sequences: A017675 A017676 A017677 * A017679 A017680 A017681 KEYWORD nonn,frac AUTHOR N. J. A. Sloane STATUS approved

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Last modified March 2 02:30 EST 2024. Contains 370447 sequences. (Running on oeis4.)