25 × 5 × 23
1, 2, 4, 5, 8, 10, 16, 20, 23, 32, 40, 46, 80, 92, 115, 160, 184, 230, 368, 460, 736, 920, 1840 and 3680
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.