cp's OEIS Frontend

A357600 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.

%I A357600 #18 Oct 07 2022 09:15:31
%S A357600 163,427,907,1555,2683,3763,5923,5947,10627,13843,15667,17803,20563,
%T A357600 30067,34483,31243,37123,48427,38707,58507,61483,85507,90787,111763,
%U A357600 93307,103027,103387,126043,166147,134467,133387,164803,222643,189883,210907,217627,158923,289963,253507
%N A357600 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 A357600 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 A357600 Conjecture: all terms are odd.
%H A357600 Jianing Song, <a href="/A357600/b357600.txt">Table of n, a(n) for n = 1..100</a>
%e A357600 Let h(D) denote the class number of the quadratic field with discriminant D.
%e A357600     n | Largest number k such | k' = largest number k |   C(-k')
%e A357600       |    that C(-k) = C_n   |  such that h(-k) = n  |
%e A357600   ----+-----------------------+-----------------------+----------
%e A357600     8 |                  5947 |                  6307 |  C_2 X C_4
%e A357600    48 |                333547 |                335203 | C_2 X C_24
%e A357600    52 |                435163 |                439147 | C_2 X C_26
%e A357600    64 |                680947 |                693067 | C_2 X C_32
%e A357600    68 |                780187 |                819163 | C_2 X C_34
%e A357600    96 |               1681243 |               1684027 | C_2 X C_48
%Y A357600 Cf. A038552, A344073.
%K A357600 nonn,hard
%O A357600 1,1
%A A357600 _Jianing Song_, Oct 05 2022