3 × 7 × 11 × 13 × 37
1, 3, 7, 11, 13, 21, 33, 37, 39, 77, 91, 111, 143, 231, 259, 273, 407, 429, 481, 777, 1001, 1221, 1443, 2849, 3003, 3367, 5291, 8547, 10101, 15873, 37037 and 111111
No.
Its nearest Fibonacci number neighbors are 75025 and 121393.