2 × 32 × 17 × 19
1, 2, 3, 6, 9, 17, 18, 19, 34, 38, 51, 57, 102, 114, 153, 171, 306, 323, 342, 646, 969, 1938, 2907 and 5814
No.
Its nearest Fibonacci number neighbors are 4181 and 6765.