Longge's problem
Description:
Longge is good at mathematics and he likes to think about hard mathematical problems which will be solved by some graceful algorithms. Now a problem comes: Given an integer N(1 < N < 2^31),you are to calculate ∑gcd(i, N) 1<=i <=N.
"Oh, I know, I know!" Longge shouts! But do you know? Please solve it.
Input:
Input contain several test case.
A number N per line.
Output:
For each N, output ,∑gcd(i, N) 1<=i <=N, a line
Sample Input:
2 6
Sample Output:
3 15
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