SP5971 LCMSUM - LCM Sum

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 Format

The first line contains T the number of test cases. Each of the next T lines contain an integer n.

Output Format

Output T lines, one for each test case, containing the required sum.