3.3 Friends for factorization
(RankList for this Question)
Score: 80pts
Time Limit: 3.00 sec
You are in the middle of the most boring lecture of your course (Not PCE).
You are least interested and want to do something challenging.
Your friend too , is not interested in the lecture. However he has invented a math problem ,just for fun. He takes a random number N and finds the sum of pairwise product of all its divisors. You find it very weird.

So for eg : the number is 4 , it has 3 divisors {1 , 2 , 4}
The sum of pairwise product of divisors : (1*2)+(1*4)+(2*4) = 14
Similarly for 10 it will be : (1*2)+(1*5)+(1*10)+(2*5)+(2*10)+(5*10) = 97

Now your friend challenges you to write a code for solving this problem.
You were smiling from inside , because this is what you wanted.

So your friend gives you T integers and you need to calculate the summation of the pairwise product of divisors of each number.

Constraints
1 <= T <= 102
1 <= N <= 105
Sum of N over all the test cases does not exceed 105.

Input Format
First line: denoting the test cases T
Next T lines containing a single integer

Output Format

Example 1
Input:
2
4
10

Output:
14
97

Explanation:
In the first test case ,
The number is 4 , it has 3 divisors {1 , 2 , 4}
The sum of pairwise product of divisors : (1*2)+(1*4)+(2*4) = 14