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.

163, 427, 907, 1555, 2683, 3763, 5923, 5947, 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, 210907, 217627, 158923, 289963, 253507

Offset: 1

Author

Jianing Song, Oct 05 2022

Keywords

• nonn
• hard

Comments

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, ...

Conjecture: all terms are odd.

Examples

			Let h(D) denote the class number of the quadratic field with discriminant D.
    n | Largest number k such | k' = largest number k |   C(-k')
      |    that C(-k) = C_n   |  such that h(-k) = n  |
  ----+-----------------------+-----------------------+----------
    8 |                  5947 |                  6307 |  C_2 X C_4
   48 |                333547 |                335203 | C_2 X C_24
   52 |                435163 |                439147 | C_2 X C_26
   64 |                680947 |                693067 | C_2 X C_32
   68 |                780187 |                819163 | C_2 X C_34
   96 |               1681243 |               1684027 | C_2 X C_48
		

Links

• Jianing Song, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A038552, A344073.