25 × 11 × 97
1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 97, 176, 194, 352, 388, 776, 1067, 1552, 2134, 3104, 4268, 8536, 17072 and 34144
No.
Its nearest Fibonacci number neighbors are 28657 and 46368.