23 × 3 × 5 × 17
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40, 51, 60, 68, 85, 102, 120, 136, 170, 204, 255, 340, 408, 510, 680, 1020 and 2040
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.