A000924 Class number of Q(sqrt(-n)), n squarefree.

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, 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, 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

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn
• nice
• easy

Examples

			a(10) = 4, since 14 is the 10th squarefree number and the class number of Q(sqrt(-14)) is 4.
		

References

• 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.
• Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966, pp. 425-430.
• D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 224-241.
• R. A. Mollin, Quadratics, CRC Press, 1996, Appendix D, gives a table for n <= 1999, correcting that of Borevich and Shafarevich.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• 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..10000
• Steven R. Finch, Class number theory [Cached copy, with permission of the author]
• Index entries for sequences related to quadratic fields

Crossrefs

Values of n run through A005117. Corresponding discriminants give A033197.

Cf. also A003649.

Programs

Mathematica

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 *)

PARI

lista(nn) = for (n=1, nn, if (issquarefree(n), print1(qfbclassno(-n*if((-n)%4>1, 4, 1)), ", "))); \\ Michel Marcus, Jul 08 2015

Extensions

Edited by Dean Hickerson, Mar 17 2003