25 × 7 × 17
1, 2, 4, 7, 8, 14, 16, 17, 28, 32, 34, 56, 68, 112, 119, 136, 224, 238, 272, 476, 544, 952, 1904 and 3808
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.