poj 2407 Relatives（简单欧拉函数）

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

Waterloo local 2002.07.01

 

#include<iostream>
#include<cstdio>
#include<cstring>
#include<queue>
#include<algorithm>
#include<stdlib.h>
using namespace std;
#define ll long long
ll eular(ll n){
    ll ans=1;
    for(ll i=2;i*i<=n;i++){
        if(n%i==0){
            ans*=i-1,n/=i;
            while(n%i==0){
                ans*=i;
                n/=i;
            }
        }
    }
    if(n>1) ans*=n-1;
    return ans;
}
int main()
{
    ll n;
    while(scanf("%I64d",&n)==1){
        if(n==0) break;
        ll ans=eular(n);
        printf("%I64d
",ans);
    }
    return 0;
}