32 × 5 × 7 × 13
1, 3, 5, 7, 9, 13, 15, 21, 35, 39, 45, 63, 65, 91, 105, 117, 195, 273, 315, 455, 585, 819, 1365 and 4095
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.