A091393 a(n) = Product_{ p | n } (1 + Legendre(-3,p) ).

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, 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, 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

Offset: 1

Author

N. J. A. Sloane, Mar 02 2004

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A049347, A091379, A240935.

Programs

Maple

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)];

Mathematica

a[n_] := Product[1 + KroneckerSymbol[-3, p], {p, FactorInteger[n][[;; , 1]]}];
a[1] = 1; Array[a, 100] (* Amiram Eldar, Oct 17 2022 *)

PARI

vecproduct(v) = { my(m=1); for(i=1,#v,m *= v[i]); m; };
A091393(n) = vecproduct(apply(p -> (1 + kronecker(-3,p)), factorint(n)[, 1])); \\ Antti Karttunen, Nov 18 2017

Formula

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