A106029 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=m if m=1 (mod 4), D=4*m otherwise and m<0 is the n-th squarefree number.

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

Offset

1,4

Comments

A000924 is the same except it is under the action of SL_2[Z].

Links

Table of n, a(n) for n=1..61.

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

m = -1, -2, -3, -5, -6, -7, -10, -11, -13, ...
with corresponding discriminant
D = -4, -8, -3, -20, -24, -7, -40, -11, -52, ....

Crossrefs

Cf. A000924.

Sequence in context: A024880 A029424 A061498 * A260311 A188431 A105153

Adjacent sequences: A106026 A106027 A106028 * A106030 A106031 A106032

Keyword

nonn

Author

Steven Finch, May 05 2005

Status

approved