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

1,7

Links

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

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

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 *)

Prog

(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

Crossrefs

Cf. A049347, A091379, A240935.

Sequence in context: A279210 A232243 A034876 * A359735 A284557 A182032

Adjacent sequences: A091390 A091391 A091392 * A091394 A091395 A091396

Keyword

nonn,mult

Author

N. J. A. Sloane, Mar 02 2004

Status

approved