22 × 3 × 13 × 19
1, 2, 3, 4, 6, 12, 13, 19, 26, 38, 39, 52, 57, 76, 78, 114, 156, 228, 247, 494, 741, 988, 1482 and 2964
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.