32 × 5 × 7 × 11
1, 3, 5, 7, 9, 11, 15, 21, 33, 35, 45, 55, 63, 77, 99, 105, 165, 231, 315, 385, 495, 693, 1155 and 3465
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.