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%I #15 Oct 17 2022 07:05:40
%S 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 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 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 a(n) = Product_{ p | n } (1 + Legendre(-3,p) ).
%H Antti Karttunen, <a href="/A091393/b091393.txt">Table of n, a(n) for n = 1..65537</a>
%F 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 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 a[n_] := Product[1 + KroneckerSymbol[-3, p], {p, FactorInteger[n][[;; , 1]]}];
%t a[1] = 1; Array[a, 100] (* _Amiram Eldar_, Oct 17 2022 *)
%o (PARI)
%o vecproduct(v) = { my(m=1); for(i=1,#v,m *= v[i]); m; };
%o A091393(n) = vecproduct(apply(p -> (1 + kronecker(-3,p)), factorint(n)[, 1])); \\ _Antti Karttunen_, Nov 18 2017
%Y Cf. A049347, A091379, A240935.
%K nonn,mult
%O 1,7
%A _N. J. A. Sloane_, Mar 02 2004
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