A003642 Number of genera of imaginary quadratic field with discriminant -k, k = A191483(n).

1, 1, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 4, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 4, 4, 4, 4, 2, 2, 4, 4, 2, 4, 2, 2, 4, 2, 2, 2, 4, 8, 2, 2, 4, 2, 4, 2, 2, 4, 4, 4, 2, 2, 4, 4, 2, 4, 2, 2, 4, 2, 2, 4, 8, 2, 4, 2, 4, 4, 2, 2, 4, 4, 4, 4, 2, 2, 2, 4, 2, 4, 2, 4, 8, 4, 2, 4, 2, 4, 4, 2, 2, 4, 2, 4, 4, 2, 4, 4, 4, 2, 2, 4

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn

References

• D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 224-241.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Index entries for sequences related to quadratic fields

Crossrefs

Cf. A001221 (omega), A003640, A003641, A191483.

Programs

Mathematica

2^(PrimeNu[Select[Range[1000], Mod[#, 4] == 0 && SquareFreeQ[#/4] && Mod[#, 16] != 12&]] - 1) (* Jean-François Alcover, Jul 25 2019, after Andrew Howroyd in A191483 *)

PARI

for(n=1, 1000, if(isfundamental(-n) && n%2==0, print1(2^(omega(n) - 1), ", "))) \\ Andrew Howroyd, Jul 24 2018

Formula

a(n) = 2^(omega(A191483(n)) - 1). - Jianing Song, Jul 24 2018

Extensions

Name clarified by Jianing Song, Jul 24 2018