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%I #18 Oct 17 2022 07:05:58
%S 1,0,1,0,0,0,0,0,1,0,2,0,2,0,0,0,0,0,0,0,0,0,2,0,0,0,1,0,0,0,0,0,2,0,
%T 0,0,2,0,2,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,2,0,2,0,0,0,0,0,0,0,
%U 2,0,2,0,2,0,0,0,0,0,0,0,1,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,2,0,0,0,0,0,0
%N a(n) = Product_{ p | n } (1 + Legendre(3,p) ).
%H Andrew Howroyd, <a href="/A091397/b091397.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) = 3*sqrt(3) * log(2+sqrt(3)) / (2*Pi^2) = 0.346676... . - _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,3),n=1..120)];
%t a[n_] := Times@@ (1+KroneckerSymbol[3, #]& /@ FactorInteger[n][[All, 1]]);
%t Array[a, 105] (* _Jean-François Alcover_, Apr 08 2020 *)
%o (PARI) a(n)={my(f=factor(n)[,1]); prod(i=1, #f, 1 + kronecker(3, f[i]))} \\ _Andrew Howroyd_, Jul 23 2018
%Y Cf. A091338, A091379, A091396.
%K nonn,mult
%O 1,11
%A _N. J. A. Sloane_, Mar 02 2004
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