Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #13 Sep 08 2022 08:44:43
%S 1,4194304,31381059609,17592186044416,2384185791015625,
%T 65810851921133568,3909821048582988049,73786976294838206464,
%U 984770902183611232881,1000000000000000000000,81402749386839761113321
%N Denominator of sum of -22nd 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="/A017708/b017708.txt">Table of n, a(n) for n = 1..10000</a>
%t Table[Denominator[DivisorSigma[22, n]/n^22], {n, 1, 20}] (* _G. C. Greubel_, Nov 05 2018 *)
%o (PARI) vector(20, n, denominator(sigma(n, 22)/n^22)) \\ _G. C. Greubel_, Nov 05 2018
%o (Magma) [Denominator(DivisorSigma(22,n)/n^22): n in [1..20]]; // _G. C. Greubel_, Nov 05 2018
%Y Cf. A017707.
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_