22 × 33 × 17
1, 2, 3, 4, 6, 9, 12, 17, 18, 27, 34, 36, 51, 54, 68, 102, 108, 153, 204, 306, 459, 612, 918 and 1836
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.