A035159 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -31.

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

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(-31, d).

Multiplicative with a(31^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(-31, p) = -1, and a(p^e) = e+1 if Kronecker(-31, p) = 1.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3*Pi/sqrt(31) = 1.69274009... . (End)

Mathematica

a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[-31, #] &]];
Table[a[n], {n, 1, 100}] (* G. C. Greubel, Apr 25 2018 *)

Prog

(PARI) my(m=-31); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(-31, d)); \\ Amiram Eldar, Nov 17 2023

Crossrefs

Sequence in context: A035184 A257541 A120854 * A103489 A213944 A127479

Adjacent sequences: A035156 A035157 A035158 * A035160 A035161 A035162

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Status

approved