24 × 7 × 3187
1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 3187, 6374, 12748, 22309, 25496, 44618, 50992, 89236, 178472 and 356944
No.
Its nearest Fibonacci number neighbors are 317811 and 514229.