A035146 - OEIS

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A035146

Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -44.

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

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OFFSET

1,3

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(-44, d).

Multiplicative with a(p^e) = 1 if Kronecker(-44, p) = 0 (p = 2 or 11), a(p^e) = (1+(-1)^e)/2 if Kronecker(-44, p) = -1, and a(p^e) = e+1 if Kronecker(-44, p) = 1.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3*Pi/(2*sqrt(11)) = 1.4208387... . (End)

MATHEMATICA

a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[-44, #] &]];

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

PROG

(PARI) my(m=-44); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))

(PARI) a(n) = sumdiv(n, d, kronecker(-44, d)); \\ Amiram Eldar, Nov 18 2023

CROSSREFS

Sequence in context: A140084 A243747 A105937 * A035216 A258587 A263548

Adjacent sequences: A035143 A035144 A035145 * A035147 A035148 A035149

KEYWORD

nonn,easy,mult

AUTHOR

N. J. A. Sloane

STATUS

approved