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 A017676 Denominator of sum of -6th powers of divisors of n. 3
 1, 64, 729, 4096, 15625, 23328, 117649, 262144, 531441, 100000, 1771561, 497664, 4826809, 3764768, 2278125, 16777216, 24137569, 34012224, 47045881, 32000000, 85766121, 56689952, 148035889, 95551488, 244140625, 11881376, 387420489, 240945152, 594823321 (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 Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k^6*(1 - x^k)). - Ilya Gutkovskiy, May 25 2018 EXAMPLE 1, 65/64, 730/729, 4161/4096, 15626/15625, 23725/23328, 117650/117649, 266305/262144, ... MATHEMATICA A017676[n_Integer] := Denominator[DivisorSigma[-6, n]]; A017676 /@ Range[100] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *) Table[Denominator[DivisorSigma[6, n]/n^6], {n, 1, 20}] (* G. C. Greubel, Nov 07 2018 *) PROG (PARI) vector(20, n, denominator(sigma(n, 6)/n^6)) \\ G. C. Greubel, Nov 07 2018 (Magma) [Denominator(DivisorSigma(6, n)/n^6): n in [1..20]]; // G. C. Greubel, Nov 07 2018 CROSSREFS Cf. A017675. Sequence in context: A016899 A250364 A346638 * A055015 A001014 A352052 Adjacent sequences: A017673 A017674 A017675 * A017677 A017678 A017679 KEYWORD nonn,frac AUTHOR N. J. A. Sloane STATUS approved

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Last modified August 9 11:50 EDT 2024. Contains 375042 sequences. (Running on oeis4.)