Description
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
The first line contains T the number of test cases. Each of the next T lines contain an integer n.Output
Output T lines, one for each test case, containing the required sum.Sample Input
31
2
5
Sample Output
14
55
Hint
Constraints1 <= T <= 300000
1 <= n <= 1000000
