POJ 2407Relatives

2018-01-27 11:14:41来源:cnblogs.com作者:自为风月马前卒人点击

Relatives
 Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 15566 Accepted: 7900

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`

Source

Waterloo local 2002.07.01  题目大意给定\$n\$，求出\$/varphi /left( n/right)\$直接套公式。\$/varphi /left( n/right) =n/prod ^{k}_{i=1}/left( /dfrac {p_{i}-1}{p_{i}}/right)\$注意先除再乘，否则会爆精度
`#include<iostream>#include<cstdio>#include<cmath>#include<cstring>#define LL long long using namespace std;int main(){    LL N;    while(cin>>N&&N!=0)    {        int limit=sqrt(N),ans=N;        for(int i = 2; i <= limit ; ++i)        {            if(N%i==0) ans=ans/i*(i-1);            while(N%i==0) N=N/i;        }        if(N>1) ans=ans/N*(N-1);        printf("%d/n",ans);    }    return 0;}`