26 × 3 × 13
1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 156, 192, 208, 312, 416, 624, 832, 1248 and 2496
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.