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POJ 2407Relatives

2018-06-17 21:20:07来源：未知阅读 ()

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

7
12
0

Sample Output

6
4

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;
}