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

Author

Steven Finch, May 05 2005

Keywords

• nonn

Comments

A104888 is the same except it is under the action of SL_2[Z].

Examples

			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, ....
		

Links

• 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.

Crossrefs

Cf. A104888.