A035196 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 14.

1, 1, 0, 1, 2, 0, 1, 1, 1, 2, 2, 0, 2, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 3, 2, 0, 1, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 1, 3, 0, 2, 0, 0, 4, 1, 0, 0, 0, 0, 2, 2, 1, 1, 4, 0, 2, 0, 0, 2, 0, 1, 0, 0, 0, 0, 2, 0, 0, 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(14, d).

Multiplicative with a(p^e) = 1 if Kronecker(14, p) = 0 (p = 2 or 7), a(p^e) = (1+(-1)^e)/2 if Kronecker(14, p) = -1 (p is in A038886), and a(p^e) = e+1 if Kronecker(14, p) = 1 (p is in A038885 \ {2, 7}).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(4*sqrt(14)+15)/(2*sqrt(14)) = 0.908710783123... . (End)

Mathematica

a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[14, #] &]]; Table[ a[n], {n, 1, 100}] (* G. C. Greubel, Apr 27 2018 *)

Prog

(PARI) my(m=14); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(14, d)); \\ Amiram Eldar, Nov 18 2023

Crossrefs

Cf. A038885, A038886.

Sequence in context: A029402 A330443 A268479 * A287475 A158020 A051160

Adjacent sequences: A035193 A035194 A035195 * A035197 A035198 A035199

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Status

approved