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A046125
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Number of negative fundamental discriminants having class number n.
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3
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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; internal format)
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OFFSET
| 1,1
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REFERENCES
| 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.
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LINKS
| Eric Weisstein's World of Mathematics, Class Number
Index entries for sequences related to quadratic fields
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EXAMPLE
| a(1) = 9 because the discriminants {-3,-4,-7,-8,-11,-19,-43,-67,-163} are the only ones with class number 1.
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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 *)
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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
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KEYWORD
| nonn,nice,changed
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
| Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), May 13 2003
Corrected and extended by Dean Hickerson (dean.hickerson(AT)yahoo.com), 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.
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