3 × 5 × 11 × 31 × 41
1, 3, 5, 11, 15, 31, 33, 41, 55, 93, 123, 155, 165, 205, 341, 451, 465, 615, 1023, 1271, 1353, 1705, 2255, 3813, 5115, 6355, 6765, 13981, 19065, 41943, 69905 and 209715
No.
Its nearest Fibonacci number neighbors are 196418 and 317811.