22 × 5 × 7 × 13
1, 2, 4, 5, 7, 10, 13, 14, 20, 26, 28, 35, 52, 65, 70, 91, 130, 140, 182, 260, 364, 455, 910 and 1820
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.