23 × 32 × 19
1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 36, 38, 57, 72, 76, 114, 152, 171, 228, 342, 456, 684 and 1368
No.
Its nearest Fibonacci number neighbors are 987 and 1597.