22 × 33 × 7
1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378 and 756
No.
Its nearest Fibonacci number neighbors are 610 and 987.