%I #20 Sep 08 2022 08:44:43
%S 1,32,243,1024,3125,648,16807,32768,59049,50000,161051,62208,371293,
%T 67228,253125,1048576,1419857,629856,2476099,1600000,4084101,117128,
%U 6436343,663552,9765625,5940688,14348907,307328,20511149,337500,28629151,33554432,13045131
%N Denominator of sum of -5th powers of divisors of n.
%C 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 G. C. Greubel, <a href="/A017674/b017674.txt">Table of n, a(n) for n = 1..10000</a>
%F Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k^5*(1 - x^k)). - _Ilya Gutkovskiy_, May 25 2018
%e 1, 33/32, 244/243, 1057/1024, 3126/3125, 671/648, 16808/16807, 33825/32768, 59293/59049, ...
%t Table[Denominator[DivisorSigma[-5, n]], {n,100}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 22 2011 *)
%t Table[Denominator[DivisorSigma[5, n]/n^5], {n, 1, 40}] (* _G. C. Greubel_, Nov 08 2018 *)
%o (PARI) vector(40, n, denominator(sigma(n, 5)/n^5)) \\ _G. C. Greubel_, Nov 08 2018
%o (Magma) [Denominator(DivisorSigma(5,n)/n^5): n in [1..40]]; // _G. C. Greubel_, Nov 08 2018
%Y Cf. A017673.
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_