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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796. M. Watkins, Class numbers of imaginary quadratic fields, Mathematics of Computation 73 (2004), pp. 907-938. Eric Weisstein's World of Mathematics, Class Number 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, A046002-A046016, 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 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 1-3 of Buell's paper, which has information for all values of n up to 125. STATUS approved

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Last modified December 5 03:31 EST 2020. Contains 338943 sequences. (Running on oeis4.)