25 × 3 × 97
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 97, 194, 291, 388, 582, 776, 1164, 1552, 2328, 3104, 4656 and 9312
No.
Its nearest Fibonacci number neighbors are 6765 and 10946.