

A046125


Number of negative fundamental discriminants having class number n.


3



9, 18, 16, 54, 25, 51, 31, 131, 34, 87, 41, 206, 37, 95, 68, 322, 45, 150, 47, 350, 85, 139, 68, 511, 95, 190, 93, 457, 83, 255, 73, 708, 101, 219, 103, 668, 85, 237, 115, 912, 109, 339, 106, 691, 154, 268, 107, 1365, 132, 345, 159, 770, 114, 427, 163, 1205, 179, 291
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..58.
Duncan A. Buell, Small class numbers and extreme values of Lfunctions of quadratic fields, Math. Comp., 31 (1977), 786796.
M. Watkins, Class numbers of imaginary quadratic fields, Mathematics of Computation 73 (2004), pp. 907938.
Eric Weisstein's World of Mathematics, Class Number
Index entries for sequences related to quadratic fields


EXAMPLE

a(1) = 9 because the discriminants {3,4,7,8,11,19,43,67,163} are the only ones with class number 1.


MATHEMATICA

FundamentalDiscriminantQ[n_] := n != 1 && (Mod[n, 4] == 1  ! Unequal[ Mod[n, 16], 8, 12]) && SquareFreeQ[n/2^IntegerExponent[n, 2]] (* via Eric E. Weisstein *);
k = 1; t = Table[0, {125}]; While[k < 2000001, If[ FundamentalDiscriminantQ@ k, a = NumberFieldClassNumber@ Sqrt@ k; If[a < 126, t[[a]]++]]; k++]; t (* Robert G. Wilson v Jun 01 2011 *)


CROSSREFS

Cf. A014602, A014603, A006203, A013658, A046002A046016, A048925, A056987, A081319, A038552, A191408, A191410.
Sequence in context: A109050 A103700 A158623 * A040072 A034728 A129855
Adjacent sequences: A046122 A046123 A046124 * A046126 A046127 A046128


KEYWORD

nonn,nice


AUTHOR

Eric W. Weisstein


EXTENSIONS

Edited by Robert G. Wilson v, May 13 2003
Corrected and extended by Dean Hickerson, May 20 2003. The values were obtained by transcribing and combining data from Tables 13 of Buell's paper, which has information for all values of n up to 125.


STATUS

approved



