2006 CMO 第 6 题

For positive integers $a_1,a_2 ,\ldots,a_{2006}$ such that $\frac{a_1}{a_2},\frac{a_2}{a_3},\ldots,\frac{a_{2005}}{a_{2006}}$ are pairwise distinct, find the minimum possible amount of distinct positive integers in the set $\{a_1,a_2,...,a_{2006}\}$ .

对于正整数 $a_1,a_2 ,\ldots,a_{2006}$ 使得 $\frac{a_1}{a_2},\frac{a_2}{a_3},\ldots,\frac{a_{2005}}{a_{2006}}$ 成对不同，求集合中不同正整数的最小可能数量$\{a_1,a_2,...,a_{2006}\}$ 。