欧拉函数的应用&&Relatives

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; }