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%I #14 Sep 08 2022 08:44:43
%S 1,4096,531441,16777216,244140625,1088391168,13841287201,68719476736,
%T 282429536481,500000000000,3138428376721,1486016741376,23298085122481,
%U 28346956187648,129746337890625,281474976710656
%N Denominator of sum of -12th 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="/A017688/b017688.txt">Table of n, a(n) for n = 1..10000</a>
%t Array[Denominator[Total[Divisors[#]^-12]]&,20] (* _Harvey P. Dale_, Dec 06 2012 *)
%t Table[Denominator[DivisorSigma[12, n]/n^12], {n, 1, 20}] (* _G. C. Greubel_, Nov 06 2018 *)
%o (PARI) vector(20, n, denominator(sigma(n, 12)/n^12)) \\ _G. C. Greubel_, Nov 06 2018
%o (Magma) [Denominator(DivisorSigma(12,n)/n^12): n in [1..20]]; // _G. C. Greubel_, Nov 06 2018
%Y Cf. A017687.
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_