24 × 7 × 4831
1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 4831, 9662, 19324, 33817, 38648, 67634, 77296, 135268, 270536 and 541072
No.
Its nearest Fibonacci number neighbors are 514229 and 832040.