23 × 32 × 13
1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 36, 39, 52, 72, 78, 104, 117, 156, 234, 312, 468 and 936
No.
Its nearest Fibonacci number neighbors are 610 and 987.