33 × 112 × 13
1, 3, 9, 11, 13, 27, 33, 39, 99, 117, 121, 143, 297, 351, 363, 429, 1089, 1287, 1573, 3267, 3861, 4719, 14157 and 42471
No.
Its nearest Fibonacci number neighbors are 28657 and 46368.