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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
A000924 is the same except it is under the action of SL_2[Z].
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.
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
KEYWORD
nonn
AUTHOR
Steven Finch, May 05 2005
STATUS
approved

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Last modified February 24 22:04 EST 2024. Contains 370307 sequences. (Running on oeis4.)