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A035143
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Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -47.
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3
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1, 2, 2, 3, 0, 4, 2, 4, 3, 0, 0, 6, 0, 4, 0, 5, 2, 6, 0, 0, 4, 0, 0, 8, 1, 0, 4, 6, 0, 0, 0, 6, 0, 4, 0, 9, 2, 0, 0, 0, 0, 8, 0, 0, 0, 0, 1, 10, 3, 2, 4, 0, 2, 8, 0, 8, 0, 0, 2, 0, 2, 0, 6, 7, 0, 0, 0, 6, 0, 0, 2, 12, 0, 4, 2, 0, 0, 0, 2, 0, 5
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{d|n} Kronecker(-47, d).
Multiplicative with a(47^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(-47, p) = -1, and a(p^e) = e+1 if Kronecker(-47, p) = 1.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 5*Pi/sqrt(47) = 2.291241... . (End)
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MATHEMATICA
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a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[-47, #] &]];
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PROG
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(PARI) my(m=-47); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(-47, d)); \\ Amiram Eldar, Nov 18 2023
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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