23 × 32 × 47
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 47, 72, 94, 141, 188, 282, 376, 423, 564, 846, 1128, 1692 and 3384
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.