[POJ2407]Relatives

Time Limit: 1000MS
Memory Limit: 65536K

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

7120

Sample Output

64

题意：求小于n的正整数中，与n互质的数的个数。

题解：
我…dxy….数学学渣。
求phi(n)。phi(n)为欧拉函数。
phi(n)=n∗(1−1/p1)∗(1−1/p2)∗...∗(1−1/px)
p1,p2,p3…px为n的所有质因数。

#include<iostream>#include<cstdio>#include<algorithm>#include<cstring>#include<cstdlib>#include<cmath>#define LiangJiaJun main#define ll long longusing namespace std;ll n;ll phi(ll x){   ll ans=x,now=x,lim=sqrt(x);   for(int i=2;i<=lim;i++){       if(now % i == 0){          ans=ans*(i-1)/i;          while(now % i==0)now /= i;       }   }   if(now > 1)ans = ans*(now-1)/now;   return ans;}int LiangJiaJun (){    while(scanf("%lld",&n)){        if(n == 0)break;        printf("%lld\n",phi(n));    }    return 0;}