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 A017669 Numerator of sum of -3rd powers of divisors of n. 3
 1, 9, 28, 73, 126, 7, 344, 585, 757, 567, 1332, 511, 2198, 387, 392, 4681, 4914, 757, 6860, 4599, 1376, 2997, 12168, 455, 15751, 9891, 20440, 3139, 24390, 147, 29792, 37449, 4144, 22113, 6192, 55261, 50654, 15435, 61544, 7371, 68922, 172, 79508, 24309, 10598 (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 (terms 1..1000 from Vincenzo Librandi) FORMULA Numerators of coefficients in expansion of Sum_{k>=1} x^k/(k^3*(1 - x^k)). - Ilya Gutkovskiy, May 24 2018 EXAMPLE 1, 9/8, 28/27, 73/64, 126/125, 7/6, 344/343, 585/512, 757/729, 567/500, 1332/1331, 511/432, ... MATHEMATICA Table[Numerator[DivisorSigma[-3, n]], {n, 50}] (* Vladimir Joseph Stephan Orlovsky, Jul 21 2011 *) Table[Numerator[DivisorSigma[3, n]/n^3], {n, 1, 40}] (* G. C. Greubel, Nov 08 2018 *) PROG (PARI) vector(40, n, numerator(sigma(n, 3)/n^3)) \\ G. C. Greubel, Nov 08 2018 (MAGMA) [Numerator(DivisorSigma(3, n)/n^3): n in [1..40]]; // G. C. Greubel, Nov 08 2018 CROSSREFS Cf. A017670. Sequence in context: A062451 A065959 A226333 * A277065 A001158 A171215 Adjacent sequences:  A017666 A017667 A017668 * A017670 A017671 A017672 KEYWORD nonn,frac AUTHOR STATUS approved

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Last modified December 5 15:11 EST 2019. Contains 329753 sequences. (Running on oeis4.)