【莫比乌斯反演】[CQBZOJ 2525]公约数

题目描述：
给定n请确定1<=x,y<=n中有多少gcd(x, y)=素数
详细参考请见:http://blog.csdn.net/jeremygjy/article/details/46360357
代码如下:

#include <cstdio>
#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
const long long MAXN = 10000000;
bool notprime[MAXN+10];
int prime[MAXN+10], mu[MAXN+10], sum[MAXN+10];
long long GetAns(long long u){
    long long ret = 0;
    for(int i=1;i<=u;i++){
        int last = u/(u/i);
        ret += (sum[last] - sum[i-1]) * (u/i) * (u/i);
        i = last;
    }
    return ret;
}
void Init(long long Max){
    mu[1] = 1;
    long long tmp;
    for(long long i=2;i<=Max;i++){
        if(!notprime[i]){
            mu[i] = -1;
            sum[i] = 1;
            prime[++prime[0]] = i;
        }
        for(int j=1;j<=prime[0]&&(tmp=prime[j]*i)<=Max;j++){
            notprime[tmp] = true;
            if(i%prime[j] == 0){
                mu[tmp] = 0;
                sum[tmp] = mu[i];
                break;
            }
            mu[tmp] = -mu[i];
            sum[tmp] = mu[i] - sum[i];
        }
    }
    for(int i=1;i<=Max;i++)
        sum[i] += sum[i-1];
}
int main(){
    long long n;
    cin>>n;
    Init(n);
    cout<<GetAns(n)<<endl;

    return 0;
}