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 A017685 #18 Apr 02 2024 02:56:48
%S A017685 1,2049,177148,4196353,48828126,30248021,1977326744,8594130945,
%T A017685 31381236757,50024415087,285311670612,185843885311,1792160394038,
%U A017685 506442812307,2883268288216,17600780175361,34271896307634,21433384705031,116490258898220,102450026512239,350279478046112
%N A017685 Numerator of sum of -11th powers of divisors of n.
%C A017685 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 A017685 G. C. Greubel, <a href="/A017685/b017685.txt">Table of n, a(n) for n = 1..10000</a>
%F A017685 From _Amiram Eldar_, Apr 02 2024: (Start)
%F A017685 sup_{n>=1} a(n)/A017686(n) = zeta(11) (A013669).
%F A017685 Dirichlet g.f. of a(n)/A017686(n): zeta(s)*zeta(s+11).
%F A017685 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A017686(k) = zeta(12) (A013670). (End)
%t A017685 Table[Numerator[Total[Divisors[n]^-11]],{n,20}] (* _Harvey P. Dale_, Aug 26 2012 *)
%t A017685 Table[Numerator[DivisorSigma[11, n]/n^11], {n, 1, 20}] (* _G. C. Greubel_, Nov 06 2018 *)
%o A017685 (PARI) vector(20, n, numerator(sigma(n, 11)/n^11)) \\ _G. C. Greubel_, Nov 06 2018
%o A017685 (Magma) [Numerator(DivisorSigma(11,n)/n^11): n in [1..20]]; // _G. C. Greubel_, Nov 06 2018
%Y A017685 Cf. A017686 (denominator), A013669, A013670.
%K A017685 nonn,frac
%O A017685 1,2
%A A017685 _N. J. A. Sloane_