26 × 3 × 19
1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 64, 76, 96, 114, 152, 192, 228, 304, 456, 608, 912, 1216, 1824 and 3648
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.