22 × 33 × 29
1, 2, 3, 4, 6, 9, 12, 18, 27, 29, 36, 54, 58, 87, 108, 116, 174, 261, 348, 522, 783, 1044, 1566 and 3132
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.