23 × 32 × 53
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 53, 72, 106, 159, 212, 318, 424, 477, 636, 954, 1272, 1908 and 3816
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.