22 × 33 × 13
1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 39, 52, 54, 78, 108, 117, 156, 234, 351, 468, 702 and 1404
No.
Its nearest Fibonacci number neighbors are 987 and 1597.