22 × 3 × 7 × 13
1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, 546 and 1092
No.
Its nearest Fibonacci number neighbors are 987 and 1597.