cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A017682 Denominator of sum of -9th powers of divisors of n.

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%I A017682 #14 Sep 08 2022 08:44:43
%S A017682 1,512,19683,262144,1953125,93312,40353607,134217728,387420489,
%T A017682 500000000,2357947691,1289945088,10604499373,2582630848,1423828125,
%U A017682 68719476736,118587876497,7346640384,322687697779
%N A017682 Denominator of sum of -9th powers of divisors of n.
%C A017682 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
%H A017682 G. C. Greubel, <a href="/A017682/b017682.txt">Table of n, a(n) for n = 1..10000</a>
%F A017682 Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k^9*(1 - x^k)). - _Ilya Gutkovskiy_, May 25 2018
%e A017682 1, 513/512, 19684/19683, 262657/262144, 1953126/1953125, 93499/93312, 40353608/40353607, 134480385/134217728, ...
%t A017682 Table[Denominator[DivisorSigma[9, n]/n^9], {n, 1, 20}] (* _G. C. Greubel_, Nov 07 2018 *)
%o A017682 (PARI) vector(20, n, denominator(sigma(n, 9)/n^9)) \\ _G. C. Greubel_, Nov 07 2018
%o A017682 (Magma) [Denominator(DivisorSigma(9,n)/n^9): n in [1..20]]; // _G. C. Greubel_, Nov 07 2018
%Y A017682 Cf. A017681.
%K A017682 nonn,frac
%O A017682 1,2
%A A017682 _N. J. A. Sloane_