A106031 a(n) is the number of orbits under the action of GL_2[Z] on the primitive binary quadratic forms of discriminant D, where D < 0 is the n-th fundamental discriminant.

1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 2, 1, 3, 2, 2, 3, 3, 2, 1, 3, 4, 3, 2, 4, 4, 2, 2, 5, 3, 4, 2, 5, 2, 4, 6, 4, 2, 3, 3, 4, 3, 2, 6, 2, 4, 4, 3, 6, 1, 5, 6, 4, 3, 5, 3, 2, 7

Offset

1,6

Comments

A006641 is the same except it is under the action of SL_2[Z].

Links

Table of n, a(n) for n=1..60.

S. R. Finch, Class number theory

Steven R. Finch, Class number theory [Cached copy, with permission of the author]

Jens Jonasson, Classes of integral binary quadratic forms, Master's thesis (2001), Appendix B.

Example

D = -3, -4, -7, -8, -11, -15, -19, -20, -23, -24, -31, ...,
that is, A003657 negated.

Crossrefs

Cf. A003657, A006641.

Sequence in context: A323015 A105194 A008335 * A055175 A339930 A307707

Adjacent sequences: A106028 A106029 A106030 * A106032 A106033 A106034

Keyword

nonn

Author

Steven Finch, May 05 2005

Status

approved