26 × 3 × 13 × 71
1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 71, 78, 96, 104, 142, 156, 192, 208, 213, 284, 312, 416, 426, 568, 624, 832, 852, 923, 1136, 1248, 1704, 1846, 2272, 2496, 2769, 3408, 3692, 4544, 5538, 6816, 7384, 11076, 13632, 14768, 22152, 29536, 44304, 59072, 88608 and 177216
No.
Its nearest Fibonacci number neighbors are 121393 and 196418.