%I #23 Sep 08 2022 08:44:43
%S 1,16,81,256,625,648,2401,4096,6561,5000,14641,3456,28561,19208,50625,
%T 65536,83521,104976,130321,80000,194481,117128,279841,165888,390625,
%U 228488,531441,43904,707281,202500,923521,1048576,1185921,39304,1500625,559872,1874161
%N Denominator of sum of -4th 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="/A017672/b017672.txt">Table of n, a(n) for n = 1..10000</a>
%F Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k^4*(1 - x^k)). - _Ilya Gutkovskiy_, May 24 2018
%e 1, 17/16, 82/81, 273/256, 626/625, 697/648, 2402/2401, 4369/4096, 6643/6561, 5321/5000, ...
%t Table[Denominator[DivisorSigma[-4, n]], {n, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 21 2011 *)
%t Table[Denominator[DivisorSigma[4, n]/n^4], {n, 1, 40}] (* _G. C. Greubel_, Nov 08 2018 *)
%o (PARI) vector(40, n, denominator(sigma(n, 4)/n^4)) \\ _G. C. Greubel_, Nov 08 2018
%o (Magma) [Denominator(DivisorSigma(4,n)/n^4): n in [1..40]]; // _G. C. Greubel_, Nov 08 2018
%Y Cf. A017671.
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_