

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



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
(Sage) [1] + [QuadraticField(n, 'a').class_number() for n in (0..200) if is_fundamental_discriminant(n) and not is_square(n)] # G. C. Greubel, Mar 01 2019


CROSSREFS



KEYWORD

nonn,easy,nice


AUTHOR



STATUS

approved



