23 × 32 × 569
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 569, 1138, 1707, 2276, 3414, 4552, 5121, 6828, 10242, 13656, 20484 and 40968
No.
Its nearest Fibonacci number neighbors are 28657 and 46368.