3 × 73 × 11 × 181
1, 3, 7, 11, 21, 33, 49, 77, 147, 181, 231, 343, 539, 543, 1029, 1267, 1617, 1991, 3773, 3801, 5973, 8869, 11319, 13937, 26607, 41811, 62083, 97559, 186249, 292677, 682913 and 2048739
No.
Its nearest Fibonacci number neighbors are 1346269 and 2178309.