A391418 Class number of order of real quadratic fields with discriminant D = A079896(n).

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

Offset

1,14

Comments

In other words, number of classes in the form class group quotient by {I,-I} of discriminant D, where I is the principal class. (So I corresponds to the form x^2 - (D/4)*y^2 for 4|D and x^2 - x*y - ((D-1)/4)*y^2 for D == 1 (mod 4), and -I corresponds to the form (D/4)*x^2 - y^2 for 4|D and ((D-1)/4)*x^2 - x*y - y^2 for D == 1 (mod 4)).

Links

Jianing Song, Table of n, a(n) for n = 1..10000

Prog

(PARI) for(n=2, 200, if(n%4 <= 1 && !issquare(n), print1(qfbclassno(n), ", ")))

Crossrefs

For a list of sequences related to the class numbers of real quadratic fields, see A087048.

Sequence in context: A308479 A031280 A391438 * A134870 A031286 A031276

Adjacent sequences: A391415 A391416 A391417 * A391419 A391420 A391421

Keyword

nonn,changed

Author

Jianing Song, Dec 09 2025

Status

approved