22 × 3 × 11 × 13
1, 2, 3, 4, 6, 11, 12, 13, 22, 26, 33, 39, 44, 52, 66, 78, 132, 143, 156, 286, 429, 572, 858 and 1716
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.