22 × 3 × 29 × 59
1, 2, 3, 4, 6, 12, 29, 58, 59, 87, 116, 118, 174, 177, 236, 348, 354, 708, 1711, 3422, 5133, 6844, 10266 and 20532
No.
Its nearest Fibonacci number neighbors are 17711 and 28657.