A035193 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 11.

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

Offset

1,5

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

From Amiram Eldar, Nov 18 2023: (Start)

a(n) = Sum_{d|n} Kronecker(11, d).

Multiplicative with a(11^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(11, p) = -1 (p is in A296936), and a(p^e) = e+1 if Kronecker(11, 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)/(3*sqrt(11)) = 0.60166042997... . (End)

Mathematica

a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[11, #] &]]; Table[ a[n], {n, 1, 100}] (* G. C. Greubel, Apr 27 2018 *)

Prog

(PARI) my(m=11); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(11, d)); \\ Amiram Eldar, Nov 18 2023

Crossrefs

Cf. A296935, A296936.

Sequence in context: A242041 A376996 A224937 * A004556 A263635 A373850

Adjacent sequences: A035190 A035191 A035192 * A035194 A035195 A035196

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Status

approved