A035156 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -34.

1, 1, 0, 1, 2, 0, 2, 1, 1, 2, 0, 0, 0, 2, 0, 1, 1, 1, 2, 2, 0, 0, 2, 0, 3, 0, 0, 2, 2, 0, 2, 1, 0, 1, 4, 1, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 3, 3, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 1, 0, 0, 2, 1, 0, 4, 2, 1, 0, 2, 0, 2, 0, 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 17 2023: (Start)

a(n) = Sum_{d|n} Kronecker(-34, d).

Multiplicative with a(p^e) = 1 if Kronecker(-34, p) = 0 (p = 2 or 17), a(p^e) = (1+(-1)^e)/2 if Kronecker(-34, p) = -1, and a(p^e) = e+1 if Kronecker(-34, p) = 1.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*Pi/sqrt(34) = 1.0775573... . (End)

Mathematica

a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[-34, #] &]];
Table[a[n], {n, 1, 100}] (* G. C. Greubel, Apr 25 2018 *)

Prog

(PARI) my(m=-34); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(-34, d)); \\ Amiram Eldar, Nov 17 2023

Crossrefs

Sequence in context: A295672 A308074 A024161 * A063883 A079691 A104450

Adjacent sequences: A035153 A035154 A035155 * A035157 A035158 A035159

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Status

approved