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%I #18 Apr 02 2024 08:51:29
%S 1,131073,129140164,17180000257,762939453126,1410565726331,
%T 232630513987208,2251816993685505,16677181828806733,50000381469792099,
%U 505447028499293772,554657012677255537,8650415919381337934,3811447419980664273,32842042032920650888,295150156996346511361
%N Numerator of sum of -17th 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="/A017697/b017697.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)/A017698(n) = zeta(17) (A013675).
%F Dirichlet g.f. of a(n)/A017698(n): zeta(s)*zeta(s+17).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A017698(k) = zeta(18) (A013676). (End)
%t Table[Numerator[DivisorSigma[17, n]/n^17], {n, 1, 20}] (* _G. C. Greubel_, Nov 05 2018 *)
%o (PARI) vector(20, n, numerator(sigma(n, 17)/n^17)) \\ _G. C. Greubel_, Nov 05 2018
%o (Magma) [Numerator(DivisorSigma(17,n)/n^17): n in [1..20]]; // _G. C. Greubel_, Nov 05 2018
%Y Cf. A017698 (denominator), A013675, A013676.
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_
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