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 A355837 #19 Jul 09 2025 04:59:30
%S A355837 1,-2,-2,0,-2,4,-2,2,0,4,-2,0,-2,4,4,0,-2,0,-2,0,4,4,-2,-4,0,4,2,0,-2,
%T A355837 -8,-2,-2,4,4,4,0,-2,4,4,-4,-2,-8,-2,0,0,4,-2,0,0,0,4,0,-2,-4,4,-4,4,
%U A355837 4,-2,0,-2,4,0,0,4,-8,-2,0,4,-8,-2,0,-2,4,0,0,4,-8,-2,0,0,4,-2,0,4,4,4,-4,-2,0,4,0,4,4,4,4
%N A355837 Dirichlet inverse of A322327.
%H A355837 Antti Karttunen, <a href="/A355837/b355837.txt">Table of n, a(n) for n = 1..100000</a>
%H A355837 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A355837 Multiplicative with a(p^e) = 2 * (e mod 2) * (-1)^((e+1)/2) for prime p and e>0.
%F A355837 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A322327(n/d) * a(d).
%F A355837 Dirichlet g.f.: zeta(4*s)/(zeta(s)^2*zeta(2*s)). - _Amiram Eldar_, Dec 29 2022
%t A355837 f[p_, e_] := 2 * (-1)^((e + 1)/2) * Mod[e, 2]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Jul 19 2022 *)
%o A355837 (PARI) A355837(n) = factorback(apply(e -> 2*(e%2)*((-1)^((1+e)/2)), factor(n)[, 2]));
%Y A355837 Cf. A322327.
%K A355837 sign,mult
%O A355837 1,2
%A A355837 _Antti Karttunen_, Jul 19 2022, based on _Werner Schulte_'s comment in A322327