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.

A017680 Denominator of sum of -8th powers of divisors of n.

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%I A017680 #16 Sep 08 2022 08:44:43
%S A017680 1,256,6561,65536,390625,839808,5764801,16777216,43046721,50000000,
%T A017680 214358881,71663616,815730721,737894528,2562890625,4294967296,
%U A017680 6975757441,11019960576,16983563041,12800000000
%N A017680 Denominator of sum of -8th powers of divisors of n.
%C A017680 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 A017680 G. C. Greubel, <a href="/A017680/b017680.txt">Table of n, a(n) for n = 1..10000</a>
%F A017680 Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k^8*(1 - x^k)). - _Ilya Gutkovskiy_, May 25 2018
%e A017680 1, 257/256, 6562/6561, 65793/65536, 390626/390625, 843217/839808, 5764802/5764801, 16843009/16777216, ...
%t A017680 Table[Denominator[Total[1/Divisors[n]^8]],{n,20}] (* _Harvey P. Dale_, Dec 16 2013 *)
%t A017680 Table[Denominator[DivisorSigma[8, n]/n^8], {n, 1, 20}] (* _G. C. Greubel_, Nov 07 2018 *)
%o A017680 (PARI) vector(20, n, denominator(sigma(n, 8)/n^8)) \\ _G. C. Greubel_, Nov 07 2018
%o A017680 (Magma) [Denominator(DivisorSigma(8,n)/n^8): n in [1..20]]; // _G. C. Greubel_, Nov 07 2018
%Y A017680 Cf. A017679.
%K A017680 nonn,frac
%O A017680 1,2
%A A017680 _N. J. A. Sloane_