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A035147 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s) + Kronecker(m,p)*p^(-2s))^(-1) for m = -43. 7
1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,11

COMMENTS

From Jianing Song, Sep 07 2018: (Start)

Half of the number of integer solutions to x^2 + x*y + 11*y^2 = n.

Inverse Moebius transform of A011591. (End)

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

FORMULA

From Jianing Song, Sep 07 2018: (Start)

a(n) is multiplicative with a(43^e) = 1, a(p^e) = (1 + (-1)^e) / 2 if Kronecker(-43, p) = -1, a(p^e) = e + 1 if Kronecker(-43, p) = 1.

G.f.: Sum_{k>0} Kronecker(-43, k) * x^k / (1 - x^k).

A138811(n) = 2 * a(n) unless n = 0.

(End)

MATHEMATICA

a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[-43, #] &]];

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

PROG

(PARI) m=-43; direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))

CROSSREFS

Cf. A138811.

Moebius transform gives A011591.

Sequence in context: A030219 A287345 A260675 * A101673 A091395 A248107

Adjacent sequences:  A035144 A035145 A035146 * A035148 A035149 A035150

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 7 07:57 EST 2021. Contains 349571 sequences. (Running on oeis4.)