2407 Relatives 欧拉函数

最新推荐文章于 2025-11-19 16:37:20 发布

原创最新推荐文章于 2025-11-19 16:37:20 发布 · 441 阅读

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文章标签：

#output #integer #input #each #less

本文介绍了一种通过编程计算小于给定正整数n并与n互质的正整数的数量的方法。提供了一个C语言实现的例子，该算法适用于不超过10亿的输入值。

Relatives

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 5921		Accepted: 2606

Description

Given n, a positive integer, how many positive integers less than n are relatively prime to n? Two integers a and b are relatively prime if there are no integers x > 1, y > 0, z > 0 such that a = xy and b = xz.

Input

There are several test cases. For each test case, standard input contains a line with n <= 1,000,000,000. A line containing 0 follows the last case.

Output

For each test case there should be single line of output answering the question posed above.

Sample Input

7
12
0

Sample Output

6
4

#include<stdio.h>
int main()
{
    int n,k;
    while(scanf("%d",&n)&&n)
    {
        int b=n;k=2;
        int res=n;
        while(k<=b)
        {
            if(b%k==0)
            {
                res-=res/k;
                b/=k;
            }
            while(b%k==0) b/=k;
            if(b==1) break;
            k++;
        }
        if(b==n) {printf("%d/n",n-1);continue;}
        if(b>1&&b<n) res-=res/k;
  printf("%d/n",res);
    }
    return 0;
}