BZOJ4805: 欧拉函数求和

#include<iostream>
#include<algorithm>
#include<cstdio>
#include<map>
#define MAXN 1700010
using namespace std;
map<int,long long> sum;
int k=0,prime[MAXN],mu[MAXN];
bool np[MAXN];
inline long long read(){
	long long date=0;char c=0;
	while(c<‘0‘||c>‘9‘)c=getchar();
	while(c>=‘0‘&&c<=‘9‘){date=date*10+c-‘0‘;c=getchar();}
	return date;
}
void make(){
	int m=MAXN-10;
	mu[1]=1;
	for(int i=2;i<=m;i++){
		if(!np[i]){
			prime[++k]=i;
			mu[i]=-1;
		}
		for(int j=1;j<=k&&prime[j]*i<=m;j++){
			np[prime[j]*i]=true;
			if(i%prime[j]==0)break;
			mu[prime[j]*i]=-mu[i];
		}
	}
	for(int i=2;i<=m;i++)mu[i]+=mu[i-1];
}
long long solve_mu(long long n){
	if(n<=MAXN-10)return mu[n];
	if(sum.count(n))return sum[n];
	long long ans=1;
	for(long long i=2,last;i<=n;i=last+1){
		last=n/(n/i);
		ans-=1LL*(last-i+1)*solve_mu(n/i);
	}
	sum[n]=ans;
	return ans;
}
long long solve_phi(long long n){
	long long ans=0;
	for(int i=1,last;i<=n;i=last+1){
		last=n/(n/i);
		ans+=1LL*(n/i)*(n/i)*(solve_mu(last)-solve_mu(i-1));
	}
	return (((ans-1)>>1)+1);
}
int main(){
	long long n=read();
	make();
	printf("%lld\n",solve_phi(n));
	return 0;
}