A091399 - OEIS

%I #14 Oct 17 2022 07:06:02

%S 1,2,2,2,0,4,1,2,2,0,0,4,0,2,0,2,0,4,2,0,2,0,0,4,0,0,2,2,2,0,2,2,0,0,

%T 0,4,2,4,0,0,0,4,0,0,0,0,2,4,1,0,0,0,2,4,0,2,4,4,2,0,0,4,2,2,0,0,0,0,

%U 0,0,0,4,0,4,0,4,0,0,0,0,2,0,2,4,0,0,4,0,0,0,0,0,4,4,0,4,0,2,0,0,0,0,2,0,0

%N a(n) = Product_{ p | n } (1 + Legendre(7,p) ).

%H Andrew Howroyd, <a href="/A091399/b091399.txt">Table of n, a(n) for n = 1..1000</a>

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 7*sqrt(7) * log(8+3*sqrt(7))/(4*Pi^2) = 1.298843... . - _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,7),n=1..120)];

%t a[1] = 1; a[n_] := Product[1+JacobiSymbol[7, p], {p, FactorInteger[n][[All, 1]]}];

%t Array[a, 105] (* _Jean-François Alcover_, Aug 26 2019 *)

%o (PARI) a(n)={my(f=factor(n)[,1]); prod(i=1, #f, 1 + kronecker(7, f[i]))} \\ _Andrew Howroyd_, Jul 23 2018

%Y Cf. A089509, A091379, A091396.

%K nonn,mult

%O 1,2

%A _N. J. A. Sloane_, Mar 02 2004