%I #18 Oct 07 2022 09:15:31
%S 163,427,907,1555,2683,3763,5923,5947,10627,13843,15667,17803,20563,
%T 30067,34483,31243,37123,48427,38707,58507,61483,85507,90787,111763,
%U 93307,103027,103387,126043,166147,134467,133387,164803,222643,189883,210907,217627,158923,289963,253507
%N Largest number k such that C(-k) is the cyclic group of order n, where C(D) is the class group of the quadratic field with discriminant D; or 0 if no such k exists.
%C Different from the largest absolute value of negative fundamental discriminant d for class number n (which is equal to A038552(n) for n <= 100) at indices 8, 48, 52, 64, 68, 96, ...
%C Conjecture: all terms are odd.
%H Jianing Song, <a href="/A357600/b357600.txt">Table of n, a(n) for n = 1..100</a>
%e Let h(D) denote the class number of the quadratic field with discriminant D.
%e n | Largest number k such | k' = largest number k | C(-k')
%e | that C(-k) = C_n | such that h(-k) = n |
%e ----+-----------------------+-----------------------+----------
%e 8 | 5947 | 6307 | C_2 X C_4
%e 48 | 333547 | 335203 | C_2 X C_24
%e 52 | 435163 | 439147 | C_2 X C_26
%e 64 | 680947 | 693067 | C_2 X C_32
%e 68 | 780187 | 819163 | C_2 X C_34
%e 96 | 1681243 | 1684027 | C_2 X C_48
%Y Cf. A038552, A344073.
%K nonn,hard
%O 1,1
%A _Jianing Song_, Oct 05 2022