

A014600


Class numbers h(D) of imaginary quadratic orders with discriminant D == 0 or 1 mod 4, D<0.


5



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

0,7


COMMENTS

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 nonmaximal 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


REFERENCES

H. Cohen, Course in Computational Alg. No. Theory, Springer, 1993, pp. 5145.


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000
S. R. Finch, Class number theory
Steven R. Finch, Class number theory [Cached copy, with permission of the author]
Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.


MATHEMATICA

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 *)


PROG

(PARI) a(n)=qfbclassno(n\2*4n%23) \\ Charles R Greathouse IV, Apr 25 2013
(PARI) a(n)=quadclassunit(n\2*4n%23).no \\ Charles R Greathouse IV, Apr 25 2013


CROSSREFS

Sequence in context: A285202 A004737 A255616 * A165475 A341456 A319420
Adjacent sequences: A014597 A014598 A014599 * A014601 A014602 A014603


KEYWORD

nonn


AUTHOR

Eric Rains (rains(AT)caltech.edu)


EXTENSIONS

Name corrected by David Jao, Sep 13 2020


STATUS

approved



