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 A383795 #15 May 24 2025 02:15:51
%S A383795 1,2,2,7,2,4,2,12,12,4,2,14,2,4,4,33,2,24,2,14,4,4,2,24,28,4,22,14,2,
%T A383795 8,2,54,4,4,4,84,2,4,4,24,2,8,2,14,24,4,2,66,52,56,4,14,2,44,4,24,4,4,
%U A383795 2,28,2,4,24,139,4,8,2,14,4,8,2,144,2,4,56,14,4,8,2,66,113
%N A383795 Dirichlet g.f.: zeta(2*s-2) * zeta(s)^2.
%H A383795 Vaclav Kotesovec, <a href="/A383795/b383795.txt">Table of n, a(n) for n = 1..10000</a>
%F A383795 Sum_{k=1..n} a(k) ~ zeta(3/2)^2 * n^(3/2)/3 - n*(log(n) + 2*log(2*Pi) + 2*gamma - 1)/2, where gamma is the Euler-Mascheroni constant A001620.
%F A383795 Multiplicative with a(p^e) = Sum_{k=0..(e-1)/2} (e+1-2*k) * p^(2*k) if e is odd, and Sum_{k=0..e/2} (e+1-2*k) * p^(2*k) if e is even. - _Amiram Eldar_, May 24 2025
%t A383795 f[p_, e_] := If[OddQ[e], Sum[(e+1-2*k) * p^(2*k), {k, 0, (e-1)/2}], Sum[(e+1-2*k) * p^(2*k), {k, 0, e/2}]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, May 24 2025 *)
%o A383795 (PARI) for(n=1, 100, print1(direuler(p=2, n, 1/((1-p^2*X^2)*(1-X)^2))[n], ", "))
%Y A383795 Cf. A035316, A057521.
%K A383795 nonn,mult
%O A383795 1,2
%A A383795 _Vaclav Kotesovec_, May 10 2025