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

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

Author

N. J. A. Sloane and Mira Bernstein

Keywords

• nonn

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

Crossrefs

Cf. A000924.

Programs

Mathematica

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

PARI

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