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 A383705 #11 May 06 2025 17:10:31
%S A383705 1,2,2,5,2,4,2,40,5,4,2,10,2,4,4,110,2,10,2,10,4,4,2,80,5,4,40,10,2,8,
%T A383705 2,308,4,4,4,25,2,4,4,80,2,8,2,10,10,4,2,220,5,10,4,10,2,80,4,80,4,4,
%U A383705 2,20,2,4,10,2618,4,8,2,10,4,8,2,200,2,4,10,10,4
%N A383705 Numerator of Dirichlet g.f.: Sum_{n>=1} a(n)/n^s = zeta(s)^(2/3).
%H A383705 Vaclav Kotesovec, <a href="/A383705/b383705.txt">Table of n, a(n) for n = 1..10000</a>
%F A383705 Sum_{k=1..n} a(k)/A256689(k) ~ n / (Gamma(2/3) * log(n)^(1/3)) * (1 + (1 - 2*gamma/3)/(3*log(n))), where gamma is the Euler-Mascheroni constant A001620 and Gamma() is the gamma function.
%t A383705 coeff=CoefficientList[Series[1/(1-x)^(2/3),{x,0,20}]//Normal,x];dptTerm[n_]:=Module[{flist=FactorInteger[n]},If[n==1,coeff[[1]],Numerator[Times@@(coeff[[flist[[All,2]]+1]])]]];Array[dptTerm,77] (* _Shenghui Yang_, May 06 2025 *)
%o A383705 (PARI) for(n=1, 100, print1(numerator(direuler(p=2, n, 1/(1-X)^(2/3))[n]), ", "))
%Y A383705 Cf. A256689 (denominator).
%Y A383705 Cf. A046643, A256688, A383657.
%K A383705 nonn,frac,mult
%O A383705 1,2
%A A383705 _Vaclav Kotesovec_, May 06 2025