A003652 Class number of real quadratic field with discriminant A003658(n), n >= 2. (Formerly M0051)

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

Offset

2,12

References

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

H. Cohen, A Course in Computational Algebraic Number Theory, Springer, 1993, pp. 515-519

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 = 2..3001

S. R. Finch, Class number theory

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

Eric Weisstein's World of Mathematics, Class Number

Mathematica

NumberFieldClassNumber[Sqrt[#]] &/@ Select[Range[500], FundamentalDiscriminantQ] (* G. C. Greubel, Mar 01 2019 *)

Prog

(PARI) for(n=1, 500, if(isfundamental(n) && !issquare(n), print1(quadclassunit(n).no, ", "))) \\ G. C. Greubel, Mar 01 2019
(Sage) [QuadraticField(n, 'a').class_number() for n in (1..500) if is_fundamental_discriminant(n) and not is_square(n)] # G. C. Greubel, Mar 01 2019

Crossrefs

Sequence in context: A336137 A371735 A088323 * A071625 A331592 A353745

Adjacent sequences: A003649 A003650 A003651 * A003653 A003654 A003655

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Extensions

Offset corrected by Jianing Song, Mar 31 2019

Status

approved