A035161 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -29.

1, 0, 2, 1, 2, 0, 0, 0, 3, 0, 2, 2, 2, 0, 4, 1, 0, 0, 2, 2, 0, 0, 0, 0, 3, 0, 4, 0, 1, 0, 2, 0, 4, 0, 0, 3, 0, 0, 4, 0, 0, 0, 2, 2, 6, 0, 2, 2, 1, 0, 0, 2, 2, 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 0, 0, 2, 2, 5

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

From Amiram Eldar, Nov 17 2023: (Start)

a(n) = Sum_{d|n} Kronecker(-29, d).

Multiplicative with a(29^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(-29, p) = -1, and a(p^e) = e+1 if Kronecker(-29, p) = 1.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*Pi/sqrt(29) = 1.166758... . (End)

Mathematica

a[n_] := DivisorSum[n, KroneckerSymbol[-29, #] &]; Array[a, 100] (* Amiram Eldar, Nov 17 2023 *)

Prog

(PARI) my(m = -29); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(-29, d)); \\ Amiram Eldar, Nov 17 2023

Crossrefs

Sequence in context: A057595 A035201 A035179 * A352565 A035186 A035194

Adjacent sequences: A035158 A035159 A035160 * A035162 A035163 A035164

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Status

approved