A091396 a(n) = Product_{ p | n } (1 + Legendre(2,p) ).

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

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. A091337, A091379, A091397, A091398, A091399.

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,2),n=1..120)];

Mathematica

a[n_] := If[n == 1, 1, Product[1 + KroneckerSymbol[2, p], {p, FactorInteger[n][[All, 1]]}]];
a /@ Range[1, 100] (* Jean-François Alcover, Sep 20 2019 *)

PARI

a(n)={my(f=factor(n)[,1]); prod(i=1, #f, 1 + kronecker(2, f[i]))} \\ Andrew Howroyd, Jul 23 2018

Formula

Multiplicative with a(2^e)=1, a(p^e)=0 if p mod 8=3 or p mod 8=5 and a(p^e)=2 if p mod 8=1 or p mod 8=7. - Vladeta Jovovic, Mar 02 2004

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 4*sqrt(2) * log(1+sqrt(2))/Pi^2 = 0.505167... . - Amiram Eldar, Oct 17 2022