%I M0195 N0072 #43 Dec 22 2021 00:10:28
%S 1,1,1,2,2,1,2,1,2,4,2,4,1,4,2,3,6,6,4,3,4,4,2,2,6,4,8,4,1,4,5,2,6,4,
%T 4,2,3,6,8,8,8,1,8,4,7,4,10,8,4,5,4,3,4,10,6,12,2,4,8,8,4,14,4,5,8,6,
%U 3,6,12,8,8,8,2,6,10,10,2,5,12,4,5,4,14,8,8,3,8,4,10,8,16,14,7,8,4,6,8,10
%N Class number of Q(sqrt(-n)), n squarefree.
%D Şaban Alaca & Kenneth S. Williams, Introductory Algebraic Number Theory. Cambridge: Cambridge University Press (2004): 322-325, Theorem 12.6.1, Example 12.6.6, Table 7.
%D Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966, pp. 425-430.
%D D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 224-241.
%D R. A. Mollin, Quadratics, CRC Press, 1996, Appendix D, gives a table for n <= 1999, correcting that of Borevich and Shafarevich.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A000924/b000924.txt">Table of n, a(n) for n = 1..10000</a>
%H Steven R. Finch, <a href="/A000924/a000924.pdf">Class number theory</a> [Cached copy, with permission of the author]
%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%e a(10) = 4, since 14 is the 10th squarefree number and the class number of Q(sqrt(-14)) is 4.
%t nmax = 100; s = Select[Range[2 * nmax], SquareFreeQ]; a[n_] := NumberFieldClassNumber[Sqrt[-s[[n]]]]; Table[a[n], {n, nmax}] (* _Jean-François Alcover_, Dec 30 2011 *)
%o (PARI) lista(nn) = for (n=1, nn, if (issquarefree(n), print1(qfbclassno(-n*if((-n)%4>1, 4, 1)), ", "))); \\ _Michel Marcus_, Jul 08 2015
%Y Values of n run through A005117. Corresponding discriminants give A033197.
%Y Cf. also A003649.
%K nonn,nice,easy
%O 1,4
%A _N. J. A. Sloane_, _Mira Bernstein_
%E Edited by _Dean Hickerson_, Mar 17 2003