51nod 1222 莫比乌斯反演

思路：

yhx找的反演题

题解已经烂大街了

#pragma GCC optimize("O3")
//By SiriusRen
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int mu[],prime[],vis[],tot;
void init(){
    mu[]=;
    for(int i=;i<=;i++){
        if(!vis[i])prime[++tot]=i,mu[i]=-;
        for(int j=;j<=tot&&i*prime[j]<=;j++){
            vis[i*prime[j]]=;mu[i*prime[j]]=-mu[i];
            if(i%prime[j]==){mu[i*prime[j]]=;break;}
        }
    }
}
ll f(ll n){
    ll res=;
    for(ll i=;i*i*i<=n;res-=,i++)
        for(ll j=i;i*j*j<=n;j++)
            res+=(n/i/j-j+)*-(i==j?(n/i/j-j)*:);
    return res;
}
ll solve(ll n){
    ll res=;
    for(ll i=;i*i<=n;i++)res+=mu[i]?mu[i]*f(n/i/i):;
    return (res+n)/;
}
int main(){
    init();ll a,b;
    scanf("%lld%lld",&a,&b);
    printf("%lld\n",solve(b)-solve(a-));
}