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A014600
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Class numbers h(D) of imaginary quadratic orders with discriminant D == 0 or 1 mod 4, D<0.
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4
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1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 2, 1, 1, 3, 2, 2, 2, 4, 2, 1, 3, 5, 2, 2, 2, 4, 4, 3, 2, 4, 2, 1, 4, 7, 2, 2, 3, 5, 4, 3, 4, 6, 2, 2, 3, 8, 4, 2, 2, 5, 6, 3, 3, 8, 2, 2, 6, 10, 4, 2, 3, 5, 4, 5, 4, 6, 4, 3, 6, 10, 4, 2, 2, 7, 6, 4, 4, 10, 4, 1, 8, 11, 4, 4, 3, 6, 6, 5, 4, 8, 4, 2, 5, 13, 4, 4
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OFFSET
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0,7
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COMMENTS
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The sequence consists of class numbers of imaginary quadratic "orders", not imaginary quadratic "fields". The difference is that an imaginary quadratic order may be a non-maximal order, but a class number of an imaginary quadratic field always refers to the class number of the maximal order within that imaginary quadratic field. - David Jao, Sep 13 2020
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REFERENCES
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H. Cohen, Course in Computational Alg. No. Theory, Springer, 1993, pp. 514-5.
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LINKS
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MATHEMATICA
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ClassList[n_?Negative] :=
Select[Flatten[#, 1] &@Table[
{i, j, (j^2 - n)/(4 i)}, {i, Sqrt[-n/3]}, {j, 1 - i, i}],
Mod[#3, 1] == 0 && #3 >= # &&
GCD[##] == 1 && ! (# == #3 && #2 < 0) & @@ # &]
a[n_] := Length[ClassList[Floor[n/2]*-4 - Mod[n, 2] - 3]] (* David Jao, Sep 14 2020 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Eric Rains (rains(AT)caltech.edu)
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EXTENSIONS
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STATUS
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approved
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