23 × 32 × 73
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 73, 146, 219, 292, 438, 584, 657, 876, 1314, 1752, 2628 and 5256
No.
Its nearest Fibonacci number neighbors are 4181 and 6765.