A035226 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s) + Kronecker(m,p)*p^(-2s))^(-1) for m = 44.

1, 1, 0, 1, 2, 0, 2, 1, 1, 2, 1, 0, 0, 2, 0, 1, 0, 1, 2, 2, 0, 1, 0, 0, 3, 0, 0, 2, 0, 0, 0, 1, 0, 0, 4, 1, 2, 2, 0, 2, 0, 0, 2, 1, 2, 0, 0, 0, 3, 3, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 4, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 1

Offset

1,5

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(44, d).

Multiplicative with a(p^e) = 1 if Kronecker(44, p) = 0 (p = 2 or 11), a(p^e) = (1+(-1)^e)/2 if Kronecker(44, p) = -1 (p is in A296936), and a(p^e) = e+1 if Kronecker(44, p) = 1 (p is in A296935).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(3*sqrt(11)+10)/sqrt(44) = 0.902490644956... . (End)

Mathematica

a[n_] := DivisorSum[n, KroneckerSymbol[44, #] &]; Array[a, 100] (* Amiram Eldar, Nov 20 2023 *)

Prog

(PARI) my(m = 44); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(44, d)); \\ Amiram Eldar, Nov 20 2023

Crossrefs

Cf. A296935, A296936.

Sequence in context: A079691 A104450 A281460 * A126043 A360170 A306659

Adjacent sequences: A035223 A035224 A035225 * A035227 A035228 A035229

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Status

approved