Score : $500$ points

问题描述

已知正整数 $N$。求 $\displaystyle\sum_{i=1}^N \left[ \frac{N}{i} \right]$ 的值。

这里，对于一个实数 $x$，$[x]$ 表示不超过 $x$ 的最大整数。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Given is a positive integer $N$. Find the value $\displaystyle\sum_{i=1}^N \left[ \frac{N}{i} \right]$.

Here, for a real number $x$, $[x]$ denotes the largest integer not exceeding $x$.

Constraints

• $1 \leq N \leq 10^{12}$
• $N$ is an integer.

Input

Input is given from Standard Input in the following format:

$N$

Output

Print the answer.

Sample Input 1

3

Sample Output 1

5

We have $\left[ \frac{3}{1} \right]+\left[ \frac{3}{2} \right]+\left[ \frac{3}{3} \right]=3+1+1=5$.

Sample Input 2

10000000000

Sample Output 2

231802823220

Note that the input and output may not fit into a $32$-bit integer type.

update @ 2024/3/10 10:03:41