欧拉函数的应用&&Relatives-优快云博客

本文详细阐述了如何利用欧拉函数解决特定数学问题，具体为求解小于给定整数的所有相对质数的数量。通过提供输入样例和详细解释，文章深入浅出地介绍了欧拉函数及其在实际应用中的重要性。

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http://acm.hdu.edu.cn/webcontest/contest_showproblem.php?cid=601&pid=1009&ojid=1

Problem 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
思路：欧拉函数的应用：φ(n)=n(1-1/p1)(1-1/p2)(1-1/p3)(1-1/p4)…..(1-1/pk)

代码：

#include<iostream> #include<cmath> using namespace std; int gett(int x) { int rec=x; int m=(int)sqrt(x*1.0)+1; for(int i=2;i<m;i++) if(x%i==0) { rec=rec/i*(i-1); while(x%i==0) x/=i；//保证每一次不出现相同的素因子。 } if(x>1) rec=rec/x*(x-1); return rec; } int main() { int n; while(cin>>n&&n) { cout<<gett(n)<<endl; }return 0; }