22 × 33 × 31
1, 2, 3, 4, 6, 9, 12, 18, 27, 31, 36, 54, 62, 93, 108, 124, 186, 279, 372, 558, 837, 1116, 1674 and 3348
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.