Question 154
Suppose that positive integers $a_1, a_2, \dots, a_{2\,006}$ (some of them may be equal) satisfy the condition: any two of $\frac{a_1}{a_2}, \frac{a_2}{a_3}, \dots, \frac{a_{2\,005}}{a_{2\,006}}$ are unequal. At least how many different numbers are there in $\{a_1, a_2, \dots, a_{2\,006}\}$? (posed by Chen Yonggao)