%I #16 Apr 02 2024 08:50:02

%S 1,32769,14348908,1073774593,30517578126,13061093507,4747561509944,

%T 35185445863425,205891146443557,500015258805447,4177248169415652,

%U 3851873211923611,51185893014090758,19446605389919367,48654880101420712,1152956690052710401,2862423051509815794

%N Numerator of sum of -15th 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="/A017693/b017693.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)/A017694(n) = zeta(15) (A013673).

%F Dirichlet g.f. of a(n)/A017694(n): zeta(s)*zeta(s+15).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A017694(k) = zeta(16) (A013674). (End)

%t Table[Numerator[DivisorSigma[15, n]/n^15], {n, 1, 20}] (* _G. C. Greubel_, Nov 06 2018 *)

%o (PARI) vector(20, n, numerator(sigma(n, 15)/n^15)) \\ _G. C. Greubel_, Nov 06 2018

%o (Magma) [Numerator(DivisorSigma(15,n)/n^15): n in [1..20]]; // _G. C. Greubel_, Nov 06 2018

%Y Cf. A017694 (denominator), A013673, A013674.

%K nonn,frac

%O 1,2

%A _N. J. A. Sloane_