A035153 - OEIS

A035153

Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -37.

1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 1

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OFFSET

1,19

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(-37, d).

Multiplicative with a(37^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(-37, p) = -1, and a(p^e) = e+1 if Kronecker(-37, p) = 1.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*Pi/(3*sqrt(37)) = 0.344316... . (End)

MATHEMATICA

a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[-37, #] &]];

Table[a[n], {n, 1, 100}] (* G. C. Greubel, Apr 25 2018 *)

PROG

(PARI) my(m=-37); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))

(PARI) a(n) = sumdiv(n, d, kronecker(-37, d)); \\ Amiram Eldar, Nov 17 2023

CROSSREFS

Sequence in context: A359542 A104194 A292261 * A069847 A238532 A097249

Adjacent sequences: A035150 A035151 A035152 * A035154 A035155 A035156

KEYWORD

nonn,easy,mult

AUTHOR

N. J. A. Sloane

STATUS

approved