25 × 3 × 41
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 41, 48, 82, 96, 123, 164, 246, 328, 492, 656, 984, 1312, 1968 and 3936
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.