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Problem D
GCD Sum
Given an integer $N$, compute the sum
\[ \sum _{i \mid N} \sum _{j \mid N} \gcd (i, j) \text {.} \]Here, $\gcd (i, j)$ is the greatest common divisor of $i$ and $j$, and $i \mid N$ denotes that $i$ is a divisor of $N$.
Input
The first and only line contains the integer $N$ ($1 \le N \le 10^{14}$).
Output
Output the sum in the task description.
| Sample Input 1 | Sample Output 1 |
|---|---|
6 |
30 |
| Sample Input 2 | Sample Output 2 |
|---|---|
7 |
10 |
