23 × 32 × 37
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 37, 72, 74, 111, 148, 222, 296, 333, 444, 666, 888, 1332 and 2664
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.