A035225 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s) + Kronecker(m,p)*p^(-2s))^(-1) for m = 43.

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

Offset

1,3

Links

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

Formula

From Amiram Eldar, Nov 20 2023: (Start)

a(n) = Sum_{d|n} Kronecker(43, d).

Multiplicative with a(43^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(43, p) = -1 (p is in A038924), and a(p^e) = e+1 if Kronecker(43, p) = 1 (p is in A038923 \ {43}).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(531*sqrt(43)+3482)/(3*sqrt(43)) = 0.899590009877... . (End)

Mathematica

a[n_] := DivisorSum[n, KroneckerSymbol[43, #] &]; Array[a, 100] (* Amiram Eldar, Nov 20 2023 *)

Prog

(PARI) my(m = 43); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(43, d)); \\ Amiram Eldar, Nov 20 2023

Crossrefs

Cf. A038923, A038924.

Sequence in context: A256637 A113063 A123477 * A298931 A035219 A245716

Adjacent sequences: A035222 A035223 A035224 * A035226 A035227 A035228

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Status

approved