Score : $400$ points

问题描述

给定一个整数 $N$。找出满足以下条件的正整数对 $(i,j)$ 的数量，其中 $i$ 和 $j$ 均不大于 $N$：

• $i \times j$ 是一个完全平方数。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

You are given an integer $N$. Find the number of pairs $(i,j)$ of positive integers at most $N$ that satisfy the following condition:

• $i \times j$ is a square number.

Constraints

• $1 \le N \le 2 \times 10^5$
• $N$ is an integer.

Input

Input is given from Standard Input in the following format:

$N$

Output

Print the answer.

Sample Input 1

4

Sample Output 1

6

The six pairs $(1,1),(1,4),(2,2),(3,3),(4,1),(4,4)$ satisfy the condition.

On the other hand, $(2,3)$ does not, since $2 \times 3 =6$ is not a square number.

Sample Input 2

254

Sample Output 2

896

update @ 2024/3/10 10:49:33