GCD operations

Consider a sequence $A_1, A_2, \ldots, A_N$, where initially, $A_i = i$ for each valid $i$. You may perform any number of operations on this sequence (including zero). In one operation, you should choose two valid indices $i$ and $j$, compute the greatest common divisor of $A_i$ and $A_j$ (let's denote it by $g$), and change both $A_i$ and $A_j$ to $g$. You are given a sequence $B_1, B_2, \ldot