A006641 Class number of forms with discriminant -A003657(n), or equivalently class number of imaginary quadratic field with discriminant -A003657(n). (Formerly M0112)

1, 1, 1, 1, 1, 2, 1, 2, 3, 2, 3, 2, 4, 2, 1, 5, 2, 2, 4, 4, 3, 1, 4, 7, 5, 3, 4, 6, 2, 2, 8, 5, 6, 3, 8, 2, 6, 10, 4, 2, 5, 5, 4, 4, 3, 10, 2, 7, 6, 4, 10, 1, 8, 11, 4, 5, 8, 4, 2, 13, 4, 9, 4, 3, 6, 14, 4, 7, 5, 4, 12, 2

Offset

1,6

References

D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 224-241.

H. Cohen, Course in Computational Alg. No. Theory, Springer, 1993, p. 514.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n=1..3000

S. R. Finch, Class number theory

Steven R. Finch, Class number theory [Cached copy, with permission of the author]

Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.

Eric Weisstein's World of Mathematics, Class Number

Mathematica

FundamentalDiscriminantQ[n_Integer] := n != 1 && (Mod[n, 4] == 1 || !Unequal[ Mod[n, 16], 8, 12]) && SquareFreeQ[n/2^IntegerExponent[n, 2]] (* via Eric W. Weisstein *);
NumberFieldClassNumber@ Sqrt@ # & /@ Select[-Range@ 300, FundamentalDiscriminantQ]

Prog

(PARI) for(n=1, 300, if(isfundamental(-n), print1(quadclassunit(-n).no, ", "))) \\ Andrew Howroyd, Jul 23 2018
(Sage) [1] + [QuadraticField(-n, 'a').class_number() for n in (0..200) if is_fundamental_discriminant(-n) and not is_square(n)] # G. C. Greubel, Mar 01 2019

Crossrefs

Cf. A003657.

Sequence in context: A012265 A339765 A268835 * A191408 A115756 A067731

Adjacent sequences: A006638 A006639 A006640 * A006642 A006643 A006644

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved