Sum of LCM Problem Statement

Given an integer 'N', calculate and print the sum of the least common multiples (LCM) for each integer from 1 to N with N.

The sum is represented as:
LCM(1, N) + LCM(2, N) + ... + LCM(N, N)

Input:

The first line of input contains a single integer T, representing the number of test cases. For each test case, the first line contains a single integer N, representing the threshold number up to which LCM needs to be summed with N.

Output:

For each test case, return the calculated sum in a new line.

Example:

Input:

2
2
3

Output:

4
11

Constraints:

• 1 <= T <= 50
• 1 <= N <= 10⁴

Note:

You don’t need to print anything. The output for each test case should be calculated and returned by implementing the given function.