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A091396
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a(n) = Product_{ p | n } (1 + Legendre(2,p) ).
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5
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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
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OFFSET
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1,7
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LINKS
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FORMULA
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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
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MAPLE
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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)];
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MATHEMATICA
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a[n_] := If[n == 1, 1, Product[1 + KroneckerSymbol[2, p], {p, FactorInteger[n][[All, 1]]}]];
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PROG
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(PARI) a(n)={my(f=factor(n)[, 1]); prod(i=1, #f, 1 + kronecker(2, f[i]))} \\ Andrew Howroyd, Jul 23 2018
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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