22 × 5 × 7 × 17
1, 2, 4, 5, 7, 10, 14, 17, 20, 28, 34, 35, 68, 70, 85, 119, 140, 170, 238, 340, 476, 595, 1190 and 2380
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.