23 × 33 × 11
1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 27, 33, 36, 44, 54, 66, 72, 88, 99, 108, 132, 198, 216, 264, 297, 396, 594, 792, 1188 and 2376
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.