A091394 a(n) = Product_{ p | n } (1 + Legendre(-5,p) ).

1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4

Offset: 1

Author

N. J. A. Sloane, Mar 02 2004

Keywords

• nonn
• mult

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A091379, A226162.

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,-5),n=1..120)];

Mathematica

a[n_] := Times@@ (1+KroneckerSymbol[-5, #]& /@ FactorInteger[n][[All, 1]]);
Array[a, 105] (* Jean-François Alcover, Apr 08 2020 *)

PARI

a(n)={my(f=factor(n)[, 1]); prod(i=1, #f, 1 + kronecker(-5, f[i]))} \\ Andrew Howroyd, Jul 25 2018

Formula

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 5*sqrt(5)/(6*Pi) = 0.593135 . - Amiram Eldar, Oct 17 2022