Relatives
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
Source
欧拉函数。
代码如下：
#include<stdio.h>
int euler_phi(int p){
int phi=p;
for(int i=2;i*i<=p;i++){
if(!(p%i)){
phi=phi-phi/i;
while(!(p%i))
p/=i;
}
}
if(p>1)
phi=phi-phi/p;
return phi;
}
int main(void){
int p;
while(scanf("%d",&p),p)
printf("%d\n",euler_phi(p));
return 0;
}