The Euler Totient Function for a positive integer N is defined as the number of positive integers less than or equal to N and relatively prime to N.
For example, an algorithm to find Euler Totient Function value of N will be:
int phi(unsigned int N)
unsigned int result = 1;
for (int i=2; i < N; i++)
if (gcd(i, N) == 1)
The task is to find the sum of the Euler Totient Values of all the divisors of the given number.
The first line of input contains a single integer T denoting the number of test cases. Then T test cases follow. Each test case consists of a single line containing a positive integer N.
Corresponding to each test case, in a new line, print the sum of the Euler Totient Function values of all the divisors of the given number.
1 ≤ T ≤ 10000
1 ≤ N ≤ 106
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