A035205 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 23.

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

Offset

1,2

Links

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

Formula

From Amiram Eldar, Nov 19 2023: (Start)

a(n) = Sum_{d|n} Kronecker(23, d).

Multiplicative with a(23^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(23, p) = -1 (p is in A038898), and a(p^e) = e+1 if Kronecker(23, p) = 1 (p = 2 or p is in A297177).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(5*sqrt(23)+24)/sqrt(23) = 1.614221300924... . (End)

Mathematica

a[n_] := DivisorSum[n, KroneckerSymbol[23, #] &]; Array[a, 100] (* Amiram Eldar, Nov 19 2023 *)

Prog

(PARI) my(m = 23); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(23, d)); \\ Amiram Eldar, Nov 19 2023

Crossrefs

Cf. A038898, A297177.

Sequence in context: A345228 A357887 A359586 * A357761 A284823 A131104

Adjacent sequences: A035202 A035203 A035204 * A035206 A035207 A035208

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Status

approved