22 × 3 × 5 × 29
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 29, 30, 58, 60, 87, 116, 145, 174, 290, 348, 435, 580, 870 and 1740
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.