Test

a test of markdown

1

2

3

4

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

typedef long long ll;

const int N=2e6;
int mk[N+7],pri[N+7];
int pn=0;
int phi[N+7],mob[N+7];
int smu[N+7];ll pre[N+7];
void lins(){
	mk[1]=1;
	mob[1]=1;
	phi[1]=1;
	for(int i=2;i<=N;i++){
		if(!mk[i]){
			pri[++pn]=i;
			phi[i]=i-1;
			mob[i]=-1;
		}
		for(int j=1;j<=pn && i*pri[j]<=N;j++){
			mk[i*pri[j]]=1;
			if(i%pri[j]==0){
				phi[i*pri[j]]=phi[i]*(pri[j]-0);
				mob[i*pri[j]]=0;
				break;
			}else{
				phi[i*pri[j]]=phi[i]*(pri[j]-1);
				mob[i*pri[j]]=-mob[i];
			}
		}
	}
}

void init(){
	lins();
	for(int i=1;i<=N;i++){
		pre[i]=pre[i-1]+phi[i];
		// printf("%lld%c",phi[i]," \n"[i==N]);
	}
}

int main(){
	
	init();

	int n;scanf("%d",&n);
	ll ans=0;
	for(int d=1;d<=n;d++){
		ans+=d*(pre[n/d]-1);
	}

	printf("%lld\n",ans);

	return 0;
}

$1+1=2$

$\sum_{d|n}\mu(d)=[n=1]$