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 A338690 #21 Oct 22 2022 08:06:29
%S A338690 1,0,0,1,2,0,0,0,1,0,0,0,2,0,0,1,2,0,0,2,0,0,0,0,3,0,0,0,2,0,0,0,0,0,
%T A338690 0,1,2,0,0,0,2,0,0,0,2,0,0,0,1,0,0,2,2,0,0,0,0,0,0,0,2,0,0,1,4,0,0,2,
%U A338690 0,0,0,0,2,0,0,0,0,0,0,2,1,0,0,0,4,0,0,0,2,0,0,0,0,0,0,0,2,0,0,3
%N A338690 Inverse Moebius transform of A209615.
%C A338690 Earliest occurrence of k is A018782(k).
%H A338690 Jianing Song, <a href="/A338690/b338690.txt">Table of n, a(n) for n = 1..10000</a>
%F A338690 Multiplicative with a(p^e) = e + 1 if p == 1 (mod 4), a(p^e) = (1 + (-1)^e)/2 if p = 2 or p == 3 (mod 4).
%F A338690 a(n) = A002654(n) = A035184(n) for odd n. a(2^e * m) = a(m) for even m, 0 for odd m.
%F A338690 Dirichlet g.f.: zeta(s)*beta(s)/(1 + 2^(-s)).
%F A338690 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Pi/6 = 0.523598... (A019673). - _Amiram Eldar_, Oct 22 2022
%t A338690 f[p_, e_] := If[Mod[p, 4] == 1, e + 1, (1 + (-1)^e)/2]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 22 2022 *)
%o A338690 (PARI) a(n) = my(r=1, f=factor(n)); for(j=1, #f[, 1], my(p=f[j, 1], e=f[j, 2]); if(p%4==1, r*=e+1, if(e%2, return(0)))); r
%Y A338690 Cf. A209615, A035184 (a similar sequence), A018782, A002654, A019673.
%K A338690 nonn,easy,mult
%O A338690 1,5
%A A338690 _Jianing Song_, Apr 24 2021