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A003649
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Class number of real quadratic field Q(sqrt f), where f is the n-th squarefree number A005117(n).
(Formerly M0054)
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5
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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
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OFFSET
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2,6
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REFERENCES
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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).
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LINKS
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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
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MATHEMATICA
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DeleteCases[Table[Boole[FreeQ[FactorInteger[n], {_, k_ /; k > 2}]] * NumberFieldClassNumber[Sqrt[n]], {n, 100}], 0] (* Alonso del Arte, Aug 26 2014 *)
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PROG
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(PARI) for(n=2, 1e3, if(issquarefree(n), print1(qfbclassno(n*if(n%4>1, 4, 1))", "))) \\ Charles R Greathouse IV, Feb 19 2013
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CROSSREFS
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Cf. A000924.
Sequence in context: A193509 A331284 A331591 * A287170 A216784 A256067
Adjacent sequences: A003646 A003647 A003648 * A003650 A003651 A003652
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane and Mira Bernstein
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STATUS
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approved
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