23 × 3 × 72
1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 49, 56, 84, 98, 147, 168, 196, 294, 392, 588 and 1176
No.
Its nearest Fibonacci number neighbors are 987 and 1597.