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A000924
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Class number of Q(sqrt(-n)), n squarefree.
(Formerly M0195 N0072)
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56
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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
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OFFSET
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1,4
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REFERENCES
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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).
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LINKS
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EXAMPLE
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a(10) = 4, since 14 is the 10th squarefree number and the class number of Q(sqrt(-14)) is 4.
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MATHEMATICA
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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 *)
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PROG
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(PARI) lista(nn) = for (n=1, nn, if (issquarefree(n), print1(qfbclassno(-n*if((-n)%4>1, 4, 1)), ", "))); \\ Michel Marcus, Jul 08 2015
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CROSSREFS
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Values of n run through A005117. Corresponding discriminants give A033197.
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KEYWORD
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nonn,nice,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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