3 × 52 × 11 × 31 × 41
1, 3, 5, 11, 15, 25, 31, 33, 41, 55, 75, 93, 123, 155, 165, 205, 275, 341, 451, 465, 615, 775, 825, 1023, 1025, 1271, 1353, 1705, 2255, 2325, 3075, 3813, 5115, 6355, 6765, 8525, 11275, 13981, 19065, 25575, 31775, 33825, 41943, 69905, 95325, 209715, 349525 and 1048575
No.
Its nearest Fibonacci number neighbors are 832040 and 1346269.