72 × 11 × 13 × 37
1, 7, 11, 13, 37, 49, 77, 91, 143, 259, 407, 481, 539, 637, 1001, 1813, 2849, 3367, 5291, 7007, 19943, 23569, 37037 and 259259
No.
Its nearest Fibonacci number neighbors are 196418 and 317811.