Given an integer array nums, return the sum of the divisors of all integers in nums that have exactly $4$ divisors. If an integer has more or fewer than $4$ divisors, do not include its divisors in the sum. If no such integer exists in the array, return $0$.

Constraints:

• $1 \leq$ nums.length $\leq 10^4$

• $1 \leq$ nums[i] $\leq 10^5$

Input: nums = [15]-List[int]
Output: 24-int
Explanation: 15 has exactly four divisors, 1, 3, 5, and 15, whose sum is 24.

Input: nums = [16, 18, 25]-List[int]
Output: 0-int
Explanation: 16, 18, and 25 do not have exactly four divisors, so none contribute to the sum.

Input: nums = [8, 10, 27, 30]-List[int]
Output: 73-int
Explanation: 8 contributes 1 + 2 + 4 + 8 = 15, 10 contributes 1 + 2 + 5 + 10 = 18, and 27 contributes 1 + 3 + 9 + 27 = 40. Since 30 does not have exactly four divisors, it is excluded, giving a total of 73.

Input: nums = [14, 14, 9]-List[int]
Output: 48-int
Explanation: Each occurrence of 14 has exactly four divisors summing to 24, while 9 does not qualify. Therefore, the total is 24 + 24 = 48.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.