

A038552


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


6



163, 427, 907, 1555, 2683, 3763, 5923, 6307, 10627, 13843, 15667, 17803, 20563, 30067, 34483, 31243, 37123, 48427, 38707, 58507, 61483, 85507, 90787, 111763, 93307, 103027, 103387, 126043, 166147, 134467, 133387, 164803, 222643, 189883
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Probably all terms are odd, in which case this is also the largest absolute value of fundamental negative discriminant d for class number n.
Numbers so far are all 19 mod 24.  Ralf Stephan, Jul 07 2003


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..100
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


MATHEMATICA

<< 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


CROSSREFS

Cf. A081319, A046125.
Sequence in context: A142427 A142237 A142283 * A127883 A054466 A221903
Adjacent sequences: A038549 A038550 A038551 * A038553 A038554 A038555


KEYWORD

nonn,nice,hard


AUTHOR

Robert Brewer (rbrewerjr(AT)aol.com)


EXTENSIONS

More terms from Robert G. Wilson v, Nov 08 2001
2 more terms from 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.
Values checked against Watkins' data, which proves the values of a(n) for n = 1..100. Charles R Greathouse IV, Feb 08 2012


STATUS

approved



