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A357600
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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.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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
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CROSSREFS
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KEYWORD
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nonn,hard
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AUTHOR
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STATUS
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approved
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