33 × 7 × 19 × 73
1, 3, 7, 9, 19, 21, 27, 57, 63, 73, 133, 171, 189, 219, 399, 511, 513, 657, 1197, 1387, 1533, 1971, 3591, 4161, 4599, 9709, 12483, 13797, 29127, 37449, 87381 and 262143
No.
Its nearest Fibonacci number neighbors are 196418 and 317811.