

A006641


Class number of forms with discriminant A003657(n), or equivalently class number of imaginary quadratic field with discriminant A003657(n).
(Formerly M0112)


4



1, 1, 1, 1, 1, 2, 1, 2, 3, 2, 3, 2, 4, 2, 1, 5, 2, 2, 4, 4, 3, 1, 4, 7, 5, 3, 4, 6, 2, 2, 8, 5, 6, 3, 8, 2, 6, 10, 4, 2, 5, 5, 4, 4, 3, 10, 2, 7, 6, 4, 10, 1, 8, 11, 4, 5, 8, 4, 2, 13, 4, 9, 4, 3, 6, 14, 4, 7, 5, 4, 12, 2
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OFFSET

1,6


REFERENCES

D. A. Buell, Binary Quadratic Forms. SpringerVerlag, NY, 1989, pp. 224241.
H. Cohen, Course in Computational Alg. No. Theory, Springer, 1993, p. 514.
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=1..3000
S. R. Finch, Class number theory
Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.
Eric Weisstein's World of Mathematics, Class Number


MATHEMATICA

FundamentalDiscriminantQ[n_Integer] := n != 1 && (Mod[n, 4] == 1  !Unequal[ Mod[n, 16], 8, 12]) && SquareFreeQ[n/2^IntegerExponent[n, 2]] (* via Eric W. Weisstein *);
NumberFieldClassNumber@ Sqrt@ # & /@ Select[Range@ 300, FundamentalDiscriminantQ]


PROG

(PARI) for(n=1, 300, if(isfundamental(n), print1(quadclassunit(n).no, ", "))) \\ Andrew Howroyd, Jul 23 2018


CROSSREFS

Sequence in context: A086520 A012265 A268835 * A191408 A115756 A067731
Adjacent sequences: A006638 A006639 A006640 * A006642 A006643 A006644


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane


STATUS

approved



