23 × 11 × 31 × 61
1, 2, 4, 8, 11, 22, 31, 44, 61, 62, 88, 122, 124, 244, 248, 341, 488, 671, 682, 1342, 1364, 1891, 2684, 2728, 3782, 5368, 7564, 15128, 20801, 41602, 83204 and 166408
No.
Its nearest Fibonacci number neighbors are 121393 and 196418.