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A038552 Largest squarefree number k such that Q(sqrt(-k)) has class number n. 6


%S 163,427,907,1555,2683,3763,5923,6307,10627,13843,15667,17803,20563,

%T 30067,34483,31243,37123,48427,38707,58507,61483,85507,90787,111763,

%U 93307,103027,103387,126043,166147,134467,133387,164803,222643,189883

%N Largest squarefree number k such that Q(sqrt(-k)) has class number n.

%C Probably all terms are odd, in which case this is also the largest absolute value of fundamental negative discriminant d for class number n.

%C Numbers so far are all 19 mod 24. - _Ralf Stephan_, Jul 07 2003

%H Charles R Greathouse IV, <a href="/A038552/b038552.txt">Table of n, a(n) for n = 1..100</a>

%H Duncan A. Buell, <a href="http://dx.doi.org/10.1090/S0025-5718-1977-0439802-X">Small class numbers and extreme values of L-functions of quadratic fields</a>, Math. Comp., 31 (1977), 786-796.

%H M. Watkins, <a href="http://dx.doi.org/10.1090/S0025-5718-03-01517-5">Class numbers of imaginary quadratic fields</a>, Mathematics of Computation 73 (2004), pp. 907-938.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ClassNumber.html">Class Number</a>

%t << NumberTheory`NumberTheoryFunctions`; a = Table[0, {32} ]; Do[ If[ Mod[n, 4] != 1 || Mod[n, 4] != 2 || SquareFreeQ[n], c = ClassNumber[ -n]; If[c < 33, a[[c]] = n]], {n, 0, 250000} ]; a

%Y Cf. A081319, A046125.

%K nonn,nice,hard

%O 1,1

%A Robert Brewer (rbrewerjr(AT)aol.com)

%E More terms from _Robert G. Wilson v_, Nov 08 2001

%E 2 more terms from _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.

%E Values checked against Watkins' data, which proves the values of a(n) for n = 1..100. _Charles R Greathouse IV_, Feb 08 2012

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Last modified August 8 02:45 EDT 2020. Contains 336290 sequences. (Running on oeis4.)