25 × 3 × 11
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 66, 88, 96, 132, 176, 264, 352, 528 and 1056
No.
Its nearest Fibonacci number neighbors are 987 and 1597.