23 × 32 × 17
1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612 and 1224
No.
Its nearest Fibonacci number neighbors are 987 and 1597.