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A035177
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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 = -13.
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2
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1, 0, 0, 1, 0, 0, 2, 0, 1, 0, 2, 0, 1, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 3, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 0, 1
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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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a(n) = Sum_{d|n} Kronecker(-13, d).
Multiplicative with a(13^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(-13, p) = -1, and a(p^e) = e+1 if Kronecker(-13, p) = 1 (p is in A296926).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*Pi/(3*sqrt(13)) = 0.5808806... . (End)
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MATHEMATICA
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a[n_] := DivisorSum[n, KroneckerSymbol[-13, #] &]; Array[a, 100] (* Amiram Eldar, Nov 17 2023 *)
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PROG
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(PARI) my(m = -13); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(-13, d)); \\ Amiram Eldar, Nov 17 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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