【莫比乌斯反演】【线性筛】bzoj2005 [Noi2010]能量采集

#include<cstdio>
#include<algorithm>
using namespace std;
#define N 100000
typedef long long ll;
bool notpri[N+5];
int pri[N+5];
ll phi[N+5];
void shai_eular()//线性筛欧拉函数，顺便处理前缀和
{
	notpri[1]=1;
	phi[1]=1;
	for(int i=2;i<=N;++i){
		if(!notpri[i]){
			pri[++pri[0]]=i;
			phi[i]=(ll)(i-1);
		}
        for(int j=1;j<=pri[0] && (ll)i*(ll)pri[j]<=(ll)N;++j){
			notpri[i*pri[j]]=1;
			if(i%pri[j]==0){
				phi[i*pri[j]]=phi[i]*(ll)pri[j];
				break;
			}
			phi[i*pri[j]]=phi[i]*(ll)(pri[j]-1);
		}
	}
	for(int i=2;i<=N;++i){
		phi[i]+=phi[i-1];
	}
}
int n,m;
int main(){
	shai_eular();
	scanf("%d%d",&n,&m);
	if(n>m){
		swap(n,m);
	}
	ll ans=0;
	for(int i=1;i<=n;){
		int j1=n/(n/i);
		int j2=m/(m/i);
		int j=min(j1,j2);
		ans+=(phi[j]-phi[i-1])*(n/i)*(m/i);
		i=j+1;
	}
	printf("%lld\n",2ll*ans-(ll)n*(ll)m);
	return 0;
}