23 × 32 × 41
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 41, 72, 82, 123, 164, 246, 328, 369, 492, 738, 984, 1476 and 2952
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.