A035164 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -26.

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

Offset

1,3

Links

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

Formula

From Amiram Eldar, Nov 17 2023: (Start)

a(n) = Sum_{d|n} Kronecker(-26, d).

Multiplicative with a(p^e) = 1 if Kronecker(-26, p) = 0 (p = 2 or 13), a(p^e) = (1+(-1)^e)/2 if Kronecker(-26, p) = -1, and a(p^e) = e+1 if Kronecker(-26, p) = 1.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3*Pi/sqrt(26) = 1.84835102... . (End)

Mathematica

a[n_] := DivisorSum[n, KroneckerSymbol[-26, #] &]; Array[a, 100] (* Amiram Eldar, Nov 17 2023 *)

Prog

(PARI) my(m = -26); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(-26, d)); \\ Amiram Eldar, Nov 17 2023

Crossrefs

Sequence in context: A071414 A067148 A035228 * A023588 A175242 A355770

Adjacent sequences: A035161 A035162 A035163 * A035165 A035166 A035167

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Status

approved