22 × 33 × 37
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 37, 54, 74, 108, 111, 148, 222, 333, 444, 666, 999, 1332, 1998 and 3996
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.