Is this program O(n^2logn) or O(nlog^2(n))?
The complexity is $O(n^2)$. The reason is that the two inner loops take $O(n)$ time. The first iteration takes $i$ operations, then $i/2$, then $i/4$ until it's 0. So we need to compute the sum of $i+i/2+i/4+...+1$ operations which its upper bounded to $2i$. Finally because your outer loop is clearly $O(n)$ the total complexity is $O(n^2)$.