Maximize Number of Nice Divisors

You are given a positive integer n. Consider an array nums where nums[i] = i. You are allowed to perform the following operation any number of times:

Choose any two indices x and y (1-indexed) from the array nums. Choose a non-negative integer z and replace nums[x] and nums[y] with nums[x] * nums[y] + z. Return the maximum number of nice divisors that you can obtain.

A nice divisor is a divisor of a number where the divisor and its complement (the other divisor) are both present.