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%I #16 Apr 02 2024 03:40:20
%S 1,262145,387420490,68719738881,3814697265626,50780172175525,
%T 1628413597910450,18014467229220865,150094635684419611,
%U 100000381469752777,5559917313492231482,4437239151658178615,112455406951957393130,213440241312117457625,295578376770097015348
%N Numerator of sum of -18th 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="/A017699/b017699.txt">Table of n, a(n) for n = 1..10000</a>
%F From _Amiram Eldar_, Apr 02 2024: (Start)
%F sup_{n>=1} a(n)/A017700(n) = zeta(18) (A013676).
%F Dirichlet g.f. of a(n)/A017700(n): zeta(s)*zeta(s+18).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A017700(k) = zeta(19) (A013677). (End)
%t Table[Numerator[DivisorSigma[18, n]/n^18], {n, 1, 20}] (* _G. C. Greubel_, Nov 05 2018 *)
%o (PARI) vector(20, n, numerator(sigma(n, 18)/n^18)) \\ _G. C. Greubel_, Nov 05 2018
%o (Magma) [Numerator(DivisorSigma(18,n)/n^18): n in [1..20]]; // _G. C. Greubel_, Nov 05 2018
%Y Cf. A017700 (denominator), A013676, A013677.
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_
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