25 × 5 × 17
1, 2, 4, 5, 8, 10, 16, 17, 20, 32, 34, 40, 68, 80, 85, 136, 160, 170, 272, 340, 544, 680, 1360 and 2720
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.