2 × 32 × 13 × 29
1, 2, 3, 6, 9, 13, 18, 26, 29, 39, 58, 78, 87, 117, 174, 234, 261, 377, 522, 754, 1131, 2262, 3393 and 6786
No.
Its nearest Fibonacci number neighbors are 6765 and 10946.