A035173 - OEIS

A035173

Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -17.

1, 2, 2, 3, 0, 4, 2, 4, 3, 0, 2, 6, 2, 4, 0, 5, 1, 6, 0, 0, 4, 4, 2, 8, 1, 4, 4, 6, 0, 0, 2, 6, 4, 2, 0, 9, 0, 0, 4, 0, 0, 8, 0, 6, 0, 4, 0, 10, 3, 2, 2, 6, 2, 8, 0, 8, 0, 0, 0, 0, 0, 4, 6, 7, 0, 8, 0, 3, 4, 0, 2, 12, 0, 0, 2, 0, 4, 8, 2, 0, 5

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OFFSET

1,2

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(-17, d).

Multiplicative with a(17^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(-17, p) = -1 (p is in A296930), and a(p^e) = e+1 if Kronecker(-17, p) = 1.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 4*Pi/sqrt(17) = 3.047792... . (End)

MATHEMATICA

a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[-17, #] &]]; Table[a[n], {n, 1, 100}] (* G. C. Greubel, Jul 17 2018 *)

PROG

(PARI) my(m = -17); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))

(PARI) a(n) = sumdiv(n, d, kronecker(-17, d)); \\ Amiram Eldar, Nov 17 2023

CROSSREFS

Cf. A296930.

Sequence in context: A035189 A197118 A035143 * A263254 A257989 A095201

Adjacent sequences: A035170 A035171 A035172 * A035174 A035175 A035176

KEYWORD

nonn,easy,mult

AUTHOR

N. J. A. Sloane

STATUS

approved