A003649 Class number of real quadratic field Q(sqrt f), where f is the n-th squarefree number A005117(n). (Formerly M0054)

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 1, 4, 1, 1, 1, 1, 2, 1, 1, 3, 2, 4, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 2

Offset

2,6

References

Şaban Alaca & Kenneth S. Williams, Introductory Algebraic Number Theory. Cambridge: Cambridge University Press (2004): 322-326, Theorem 12.6.1, Example 12.6.7, Table 8.

D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 224-241.

M. Pohst and H. Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge Univ. Press, 1989, p. 432.

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..6083 (squarefree numbers < 10000)

S. R. Finch, Class number theory [Cached copy, with permission of the author]

Index entries for sequences related to quadratic fields

Mathematica

DeleteCases[Table[Boole[FreeQ[FactorInteger[n], {_, k_ /; k > 2}]] * NumberFieldClassNumber[Sqrt[n]], {n, 100}], 0] (* Alonso del Arte, Aug 26 2014 *)

Prog

(PARI) for(n=2, 1e3, if(issquarefree(n), print1(qfbclassno(n*if(n%4>1, 4, 1))", "))) \\ Charles R Greathouse IV, Feb 19 2013

Crossrefs

Cf. A000924.

Sequence in context: A193509 A331284 A331591 * A353741 A287170 A216784

Adjacent sequences: A003646 A003647 A003648 * A003650 A003651 A003652

Keyword

nonn

Author

N. J. A. Sloane and Mira Bernstein

Status

approved