23 × 32 × 31
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 31, 36, 62, 72, 93, 124, 186, 248, 279, 372, 558, 744, 1116 and 2232
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.