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

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

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn

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

Programs

Mathematica

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

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

Extensions

Offset corrected by Jianing Song, Mar 31 2019