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 A383657 #16 May 04 2025 23:44:22
%S A383657 1,3,3,15,3,9,3,35,15,9,3,45,3,9,9,315,3,45,3,45,9,9,3,105,15,9,35,45,
%T A383657 3,27,3,693,9,9,9,225,3,9,9,105,3,27,3,45,45,9,3,945,15,45,9,45,3,105,
%U A383657 9,105,9,9,3,135,3,9,45,3003,9,27,3,45,9,27,3,525,3
%N A383657 Numerator of Dirichlet g.f.: Sum_{n>=1} a(n)/n^s = zeta(s)^(3/2).
%C A383657 In general, for m > 0, if Dirichlet g.f. is zeta(s)^m, then Sum_{j=1..n} a(j) ~ n*log(n)^(m-1)/Gamma(m) * (1 + (m-1)*(m*gamma - 1)/log(n)), where gamma is the Euler-Mascheroni constant A001620 and Gamma() is the gamma function.
%H A383657 Vaclav Kotesovec, <a href="/A383657/b383657.txt">Table of n, a(n) for n = 1..10000</a>
%F A383657 Sum_{k=1..n} A383657(k)/A383658(k) ~ 2*n*sqrt(log(n)/Pi) * (1 - (1 - 3*gamma/2)/(2*log(n))), where gamma is the Euler-Mascheroni constant A001620.
%t A383657 coeff=CoefficientList[Series[1/(1-x)^(3/2),{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,73] (* _Shenghui Yang_, May 04 2025 *)
%o A383657 (PARI) for(n=1, 100, print1(numerator(direuler(p=2, n, 1/(1-X)^(3/2))[n]), ", "))
%Y A383657 Cf. A383658.
%Y A383657 Cf. A046643, A046644, A256688, A256689, A256690, A256691, A256692, A256693.
%Y A383657 Cf. A000005, A007425, A007426, A061200, A034695.
%K A383657 nonn,frac,mult
%O A383657 1,2
%A A383657 _Vaclav Kotesovec_, May 04 2025