A003642 Number of genera of imaginary quadratic field with discriminant -k, k = A191483(n). (Formerly M0211)

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

1,3

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

Table of n, a(n) for n=1..105.

Index entries for sequences related to quadratic fields

Formula

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A369978 A083261 A003648 * A100007 A104369 A051702

Adjacent sequences: A003639 A003640 A003641 * A003643 A003644 A003645

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Extensions

Name clarified by Jianing Song, Jul 24 2018

Status

approved