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 A091393 #15 Oct 17 2022 07:05:40 %S A091393 1,0,1,0,0,0,2,0,1,0,0,0,2,0,0,0,0,0,2,0,2,0,0,0,0,0,1,0,0,0,2,0,0,0, %T A091393 0,0,2,0,2,0,0,0,2,0,0,0,0,0,2,0,0,0,0,0,0,0,2,0,0,0,2,0,2,0,0,0,2,0, %U A091393 0,0,0,0,2,0,0,0,0,0,2,0,1,0,0,0,0,0,0,0,0,0,4,0,2,0,0,0,2,0,0,0,0,0,2,0,0 %N A091393 a(n) = Product_{ p | n } (1 + Legendre(-3,p) ). %H A091393 Antti Karttunen, <a href="/A091393/b091393.txt">Table of n, a(n) for n = 1..65537</a> %F A091393 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3*sqrt(3)/(4*Pi) = 0.413496... (A240935). - _Amiram Eldar_, Oct 17 2022 %p A091393 with(numtheory); L := proc(n,N) local i,t1,t2; t1 := ifactors(n)[2]; t2 := mul((1+legendre(N,t1[i][1])),i=1..nops(t1)); end; [seq(L(n,-3),n=1..120)]; %t A091393 a[n_] := Product[1 + KroneckerSymbol[-3, p], {p, FactorInteger[n][[;; , 1]]}]; %t A091393 a[1] = 1; Array[a, 100] (* _Amiram Eldar_, Oct 17 2022 *) %o A091393 (PARI) %o A091393 vecproduct(v) = { my(m=1); for(i=1,#v,m *= v[i]); m; }; %o A091393 A091393(n) = vecproduct(apply(p -> (1 + kronecker(-3,p)), factorint(n)[, 1])); \\ _Antti Karttunen_, Nov 18 2017 %Y A091393 Cf. A049347, A091379, A240935. %K A091393 nonn,mult %O A091393 1,7 %A A091393 _N. J. A. Sloane_, Mar 02 2004