23 × 32 × 29
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 29, 36, 58, 72, 87, 116, 174, 232, 261, 348, 522, 696, 1044 and 2088
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.