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A000924 Class number of Q(sqrt(-n)), n squarefree.
(Formerly M0195 N0072)
26
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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

EXAMPLE

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

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 *)

PROG

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

CROSSREFS

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

Cf. also A003649.

Sequence in context: A260311 A188431 A105153 * A305432 A305298 A298824

Adjacent sequences:  A000921 A000922 A000923 * A000925 A000926 A000927

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane, Mira Bernstein

EXTENSIONS

Edited by Dean Hickerson, Mar 17 2003

STATUS

approved

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Last modified November 19 00:12 EST 2018. Contains 317332 sequences. (Running on oeis4.)