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.

A017690 Denominator of sum of -13th powers of divisors of n.

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%I A017690 #12 Sep 08 2022 08:44:43
%S A017690 1,8192,1594323,67108864,1220703125,1088391168,96889010407,
%T A017690 549755813888,2541865828329,5000000000000,34522712143931,
%U A017690 26748301344768,302875106592253,99214346656768,648731689453125
%N A017690 Denominator of sum of -13th powers of divisors of n.
%C A017690 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 A017690 G. C. Greubel, <a href="/A017690/b017690.txt">Table of n, a(n) for n = 1..10000</a>
%t A017690 Table[Denominator[DivisorSigma[13, n]/n^13], {n, 1, 20}] (* _G. C. Greubel_, Nov 06 2018 *)
%o A017690 (PARI) vector(20, n, denominator(sigma(n, 13)/n^13)) \\ _G. C. Greubel_, Nov 06 2018
%o A017690 (Magma) [Denominator(DivisorSigma(13,n)/n^13): n in [1..20]]; // _G. C. Greubel_, Nov 06 2018
%Y A017690 Cf. A017689.
%K A017690 nonn,frac
%O A017690 1,2
%A A017690 _N. J. A. Sloane_