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A081319 Smallest squarefree integer k such that Q(sqrt(-k)) has class number n, or 0 if no such k exists.

%I A081319 #35 May 08 2021 22:54:55
%S A081319 1,5,23,14,47,26,71,41,199,74,167,89,191,101,239,146,383,293,311,194,
%T A081319 431,269,647,329,479,314,983,341,887,461,719,446,839,614,1031,626,
%U A081319 1487,1199,1439,689,1151,794,1847,854,1319,941,3023,1106,1511,1109,1559
%N A081319 Smallest squarefree integer k such that Q(sqrt(-k)) has class number n, or 0 if no such k exists.
%H A081319 Robert G. Wilson v, <a href="/A081319/b081319.txt">Table of n, a(n) for n = 1..4500</a>
%H A081319 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.
%F A081319 a(n) = A060649(n) for odd n > 1. For even n, assuming that A060649(n) > 0 and A344072(n/2) > 0, a(n) = min{A060649(n), A344072(n/2)/4}. - _Jianing Song_, May 08 2021
%e A081319 From _Jianing Song_, May 08 2021: (Start)
%e A081319 a(6) = min{A060649(6), A344072(3)/4} = min{87, 104/4} = 26.
%e A081319 a(12) = min{A060649(12), A344072(6)/4} = min{231, 356/4} = 89.
%e A081319 a(18) = min{A060649(12), A344072(9)/4} = min{335, 1172/4} = 293.
%e A081319 a(38) = min{A060649(38), A344072(19)/4} = min{1199, 4916/4} = 1199. (End)
%t A081319 t[_] := 0; k = -1; While[k > -3100, a = NumberFieldClassNumber@Sqrt@k; If[t[a] == 0, t[a] = -k; Print[{a, -k}]]; k--]; t /@ Range@51 (* _Robert G. Wilson v_, Sep 25 2017 *)
%Y A081319 Cf. A060649, A038552, A046125, A014602-A046020.
%K A081319 nonn
%O A081319 1,2
%A A081319 _Dean Hickerson_, Mar 18 2003
%E A081319 Edited by _Max Alekseyev_, Apr 28 2010
%E A081319 Escape clause added by _Jianing Song_, May 08 2021