Relatives
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 Inpu**t
7
12
0
Sample Output
6
4
题意：
给定一个数n，求所有小于等于n的正整数中，有多少个是与n互质的。
知识点：
欧拉函数(模板）
#include<stdio.h>
int oula(int n)//欧拉函数的模板
{
int i,ans=n;
for(i=2;i*i<=n;++i)
if(n%i==0){
ans-=ans/i;
while(n%i==0)
n/=i;
}
if(n>1)
ans-=ans/n;
return ans;
}
int main()
{
int n;
while(~scanf("%d",&n),n){
printf("%d\n",oula(n));
}
return 0;
}或者：
#include<stdio.h>
#include<stdlib.h>
int eular(int n)
{
int ret=1,i;
for(i=2;i*i<=n;i++)
{
if(n%i==0)
{
n/=i,ret*=i-1;
while(n%i==0) n/=i,ret*=i; //去除n个数中所有i倍数的数，并且除一次就说明有i个因数存在
}
}
if(n>1) ret*=n-1; //说明n为可以分解的最小质数那么所有比它小得数都与它互余
return ret;
}
int main ()
{
int n,s;
while(~scanf("%d",&n)&&n!=0)
{ s=0;
s=eular(n);
printf("%d\n",s);
}
return 0;
}