22 × 32 × 7 × 11
1, 2, 3, 4, 6, 7, 9, 11, 12, 14, 18, 21, 22, 28, 33, 36, 42, 44, 63, 66, 77, 84, 99, 126, 132, 154, 198, 231, 252, 308, 396, 462, 693, 924, 1386 and 2772
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.