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%I #18 Apr 02 2024 08:51:43
%S 1,8388609,94143178828,70368752566273,11920928955078126,
%T 65810859767097521,27368747340080916344,590295880727458217985,
%U 8862938119746644274757,50000005960464481733367,895430243255237372246532,1656184514187480740117011,41753905413413116367045798
%N Numerator of sum of -23rd 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="/A017709/b017709.txt">Table of n, a(n) for n = 1..1000</a>
%F From _Amiram Eldar_, Apr 02 2024: (Start)
%F sup_{n>=1} a(n)/A017710(n) = zeta(23).
%F Dirichlet g.f. of a(n)/A017710(n): zeta(s)*zeta(s+23).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A017710(k) = zeta(24). (End)
%t Table[Numerator[Total[Divisors[n]^-23]],{n,12}] (* _Harvey P. Dale_, Oct 19 2012 *)
%t Table[Numerator[DivisorSigma[23, n]/n^23], {n, 1, 20}] (* _G. C. Greubel_, Nov 03 2018 *)
%o (PARI) a(n) = numerator(sigma(n, 23)/n^23); \\ _G. C. Greubel_, Nov 03 2018
%o (Magma) [Numerator(DivisorSigma(23,n)/n^23): n in [1..20]]; // _G. C. Greubel_, Nov 03 2018
%Y Cf. A017710 (denominator).
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_
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