Problems
LCM Sum
LCM Sum
Given n, calculate the sum LCM(1, n) + LCM(2, n) + .. + LCM(n, n), where LCM(i, n) denotes the Least Common Multiple of the integers i and n.
Input
First line contains the number of test cases t (1 ≤ t ≤ 300000). Each of the next t lines contains an integer n (1 ≤ n ≤ 106
).
Output
Print t lines, one for each test case, containing the required sum.
Input example #1
3 1 2 5
Output example #1
1 4 55