A035149 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -41.

1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 0, 4, 4, 5, 0, 6, 2, 6, 4, 4, 0, 8, 3, 0, 4, 6, 0, 8, 0, 6, 4, 0, 4, 9, 2, 4, 0, 8, 1, 8, 0, 6, 6, 0, 2, 10, 3, 6, 0, 0, 0, 8, 4, 8, 4, 0, 0, 12, 2, 0, 6, 7, 0, 8, 2, 0, 0, 8, 2, 12, 2, 4, 6, 6, 4, 0, 2, 10

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

From Amiram Eldar, Nov 17 2023: (Start)

a(n) = Sum_{d|n} Kronecker(-41, d).

Multiplicative with a(41^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(-41, p) = -1, and a(p^e) = e+1 if Kronecker(-41, p) = 1.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 8*Pi/sqrt(41) = 3.925074... . (End)

Mathematica

a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[-41, #] &]];
Table[a[n], {n, 1, 100}] (* G. C. Greubel, Apr 25 2018 *)

Prog

(PARI) my(m=-41); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(-41, d)); \\ Amiram Eldar, Nov 17 2023

Crossrefs

Sequence in context: A289849 A299701 A286605 * A074848 A252505 A365173

Adjacent sequences: A035146 A035147 A035148 * A035150 A035151 A035152

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Status

approved