P15765 [JAG 2025 Summer Camp #1] Sum of Floor(N/ij)

You are given a positive integer $N$. Find the value $$\sum_{i=1}^{N} \sum_{j=1}^{N} \left\lfloor \frac{N}{ij} \right\rfloor$$ You are given $T$ test cases, so find the answer for each.

The input is given in the following format: $$\begin{aligned} & T \\ & \text{case}_1 \\ & \text{case}_2 \\ & \vdots \\ & \text{case}_T \end{aligned}$$ $\text{case}_i$ represents the $i$-th test case. Each test case is given in the following format: $$N$$ - $1 \leq T \leq 100$ - $1 \leq N \leq 10^9$ - All input values are integers.

Output $T$ lines. On the $i$-th line ($1 \leq i \leq T$), output the answer to the $i$-th test case.