26 × 5 × 7
1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 140, 160, 224, 280, 320, 448, 560, 1120 and 2240
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.