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A035143
Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -47.
3
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
OFFSET
1,2
LINKS
FORMULA
From Amiram Eldar, Nov 18 2023: (Start)
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)
MATHEMATICA
a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[-47, #] &]];
Table[a[n], {n, 1, 100}] (* G. C. Greubel, Apr 25 2018 *)
PROG
(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
CROSSREFS
Sequence in context: A071449 A035189 A197118 * A035173 A263254 A257989
KEYWORD
nonn,easy,mult
STATUS
approved