P8570 [JRKSJ R6] The Connected World.
Background
Description
Given $n, m$, find
$$\sum_{i=1}^n \sum_{j=1}^m \sigma_0(ij)\varphi(ij)$$
Input Format
Two integers $n, m$.
Output Format
Output one integer, representing the answer. The answer should be taken modulo $10^9+7$.
Explanation/Hint
$\sigma_0, \varphi$ are the divisor-counting function and Euler's totient function, respectively.
This problem may be slightly tight on constant factors.
### Constraints
This problem uses bundled subtasks.
| $\text{Subtask}$ | $n, m \le$ | $\text{Score}$ |
| :----------: | :----------: | :----------: |
| $1$ | $10^3$ | $10$ |
| $2$ | $10^5$ | $30$ |
| $3$ | $2\times 10^5$ | $30$ |
| $4$ | $5\times 10^5$ | $30$ |
| $5$ | $3\times 10^6$ | $1$ |
For all testdata, $1 \le n, m \le 3\times 10^6$.
For some reason, you only need to get $\ge 100$ points to pass this problem.
Translated by ChatGPT 5