This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A017679 #20 Apr 02 2024 02:56:08
%S A017679 1,257,6562,65793,390626,843217,5764802,16843009,43053283,50195441,
%T A017679 214358882,71955611,815730722,740777057,2563287812,4311810305,
%U A017679 6975757442,11064693731,16983563042,12850228209,37828630724,27545116337,78310985282,55261912529,152588281251
%N A017679 Numerator of sum of -8th powers of divisors of n.
%C A017679 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 A017679 G. C. Greubel, <a href="/A017679/b017679.txt">Table of n, a(n) for n = 1..10000</a>
%F A017679 Numerators of coefficients in expansion of Sum_{k>=1} x^k/(k^8*(1 - x^k)). - _Ilya Gutkovskiy_, May 25 2018
%F A017679 From _Amiram Eldar_, Apr 02 2024: (Start)
%F A017679 sup_{n>=1} a(n)/A017680(n) = zeta(8) (A013666).
%F A017679 Dirichlet g.f. of a(n)/A017680(n): zeta(s)*zeta(s+8).
%F A017679 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A017680(k) = zeta(9) (A013667). (End)
%e A017679 1, 257/256, 6562/6561, 65793/65536, 390626/390625, 843217/839808, 5764802/5764801, 16843009/16777216, ...
%t A017679 Table[Numerator[DivisorSigma[8, n]/n^8], {n, 1, 20}] (* _G. C. Greubel_, Nov 07 2018 *)
%o A017679 (PARI) vector(20, n, numerator(sigma(n, 8)/n^8)) \\ _G. C. Greubel_, Nov 07 2018
%o A017679 (Magma) [Numerator(DivisorSigma(8,n)/n^8): n in [1..20]]; // _G. C. Greubel_, Nov 07 2018
%Y A017679 Cf. A017680 (denominator), A013666, A013667.
%K A017679 nonn,frac
%O A017679 1,2
%A A017679 _N. J. A. Sloane_