POJ2407 Relatives

http://poj.org/problem?id=2407

题意：求一个大数的欧拉函数

欧拉函数

运用公式即可

\[\varphi(n)=(1-\frac{1}{p_{1}}) (1-\frac{1}{p_{2}})\cdots(1-\frac{1}{p_{m}})n \qquad(p_{i}为n的质因数) \]

\(C++ Code:\)

#include<iostream>
#include<cstdio>
#include<cmath>
#include<algorithm>
using namespace std;
long long n;
int main()
{
    for (;;)
    {
        scanf("%lld",&n);
        if (!n)
            break;
        if (n==1)
        {
            puts("0");
            continue;
        }
        long long g=n;
        long long ans=n;
        for (long long i=2;i*i<=g;i++)
            if (g%i==0)
            {
                ans=ans-ans/i;
                while (g%i==0)
                    g/=i;
            }
        if (g^1)
            ans=ans-ans/g;
        cout << ans << endl;
    }
    return 0;
}