A035247 Indices of the nonzero terms in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m= -11.
1, 3, 4, 5, 9, 11, 12, 15, 16, 20, 23, 25, 27, 31, 33, 36, 37, 44, 45, 47, 48, 49, 53, 55, 59, 60, 64, 67, 69, 71, 75, 80, 81, 89, 92, 93, 97, 99, 100, 103, 108, 111, 113, 115, 121, 124, 125, 132, 135, 137, 141, 144, 147, 148, 155, 157, 159, 163, 165, 169, 176, 177, 179, 180, 181, 185, 188, 191, 192, 196, 199
Offset: 1
Keywords
Crossrefs
Cf. A028954 (a probable duplicate). [From R. J. Mathar, Oct 20 2008]
Cf. A035179 (the expansion itself).
Programs
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Mathematica
Reap[For[n = 1, n < 200, n++, r = Reduce[x^2 + x y + 3 y^2 == n, {x, y}, Integers]; If[r =!= False, Sow[n]]]][[2, 1]] (* Jean-François Alcover, Oct 31 2016 *) -
PARI
m=-11; select(x -> x, direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X)), 1) \\ Fixed by Andrey Zabolotskiy, Jul 30 2020
Extensions
More terms from Jean-François Alcover, Oct 31 2016
Name corrected by Andrey Zabolotskiy, Jul 30 2020