23 × 3 × 5 × 19
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 19, 20, 24, 30, 38, 40, 57, 60, 76, 95, 114, 120, 152, 190, 228, 285, 380, 456, 570, 760, 1140 and 2280
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.