25 × 3 × 569
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 569, 1138, 1707, 2276, 3414, 4552, 6828, 9104, 13656, 18208, 27312 and 54624
No.
Its nearest Fibonacci number neighbors are 46368 and 75025.