22 × 3 × 5 × 587
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 587, 1174, 1761, 2348, 2935, 3522, 5870, 7044, 8805, 11740, 17610 and 35220
No.
Its nearest Fibonacci number neighbors are 28657 and 46368.