23 × 52 × 13
1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 130, 200, 260, 325, 520, 650, 1300 and 2600
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.