22 × 5 × 11 × 17
1, 2, 4, 5, 10, 11, 17, 20, 22, 34, 44, 55, 68, 85, 110, 170, 187, 220, 340, 374, 748, 935, 1870 and 3740
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.