22 × 33 × 23
1, 2, 3, 4, 6, 9, 12, 18, 23, 27, 36, 46, 54, 69, 92, 108, 138, 207, 276, 414, 621, 828, 1242 and 2484
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.