23 × 32 × 23
1, 2, 3, 4, 6, 8, 9, 12, 18, 23, 24, 36, 46, 69, 72, 92, 138, 184, 207, 276, 414, 552, 828 and 1656
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.