cp's OEIS Frontend

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

%I A003652 M0051 #32 Feb 16 2025 08:32:27
%S A003652 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,
%T A003652 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,
%U A003652 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
%N A003652 Class number of real quadratic field with discriminant A003658(n), n >= 2.
%D A003652 D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 224-241.
%D A003652 H. Cohen, A Course in Computational Algebraic Number Theory, Springer, 1993, pp. 515-519
%D A003652 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003652 T. D. Noe, <a href="/A003652/b003652.txt">Table of n, a(n) for n = 2..3001</a>
%H A003652 S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Class number theory</a>
%H A003652 Steven R. Finch, <a href="/A000924/a000924.pdf">Class number theory</a> [Cached copy, with permission of the author]
%H A003652 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number</a>
%t A003652 NumberFieldClassNumber[Sqrt[#]] &/@ Select[Range[500], FundamentalDiscriminantQ] (* _G. C. Greubel_, Mar 01 2019 *)
%o A003652 (PARI) for(n=1, 500, if(isfundamental(n) && !issquare(n), print1(quadclassunit(n).no, ", "))) \\ _G. C. Greubel_, Mar 01 2019
%o A003652 (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
%K A003652 nonn
%O A003652 2,12
%A A003652 _N. J. A. Sloane_, _Mira Bernstein_
%E A003652 Offset corrected by _Jianing Song_, Mar 31 2019