A106030 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>1 is the n-th squarefree number.

1, 2, 1, 2, 2, 2, 2, 1, 2, 4, 1, 2, 2, 2, 2, 2, 1, 4, 2, 2, 3, 4, 1, 2, 4, 1, 4, 2, 2, 2, 4, 1, 4, 2, 2, 2, 1, 2, 2, 4, 2, 2, 4, 2, 1, 2, 2, 4, 4, 3, 2, 2, 2, 4, 1, 4, 2, 2, 4, 1

Offset

1,2

Comments

A104888 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

m = 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, ...
with corresponding discriminant
D = 8, 12, 5, 24, 28, 40, 44, 13, 56, 60, 17, ....

Crossrefs

Cf. A104888.

Sequence in context: A055255 A057768 A317990 * A104888 A286885 A365618

Adjacent sequences: A106027 A106028 A106029 * A106031 A106032 A106033

Keyword

nonn

Author

Steven Finch, May 05 2005

Status

approved