欧拉函数-bzoj2818-简单推导

This article is made by Jason-Cow.
Welcome to reprint.
But please post the writer's address.

http://www.cnblogs.com/JasonCow/

 

 

/*

ans=

　　 sigma(for each prime<=n)  

　　{

　　　　{

　　　　　　simga(for i=1 to n/now prime) phi[i] 

　　　　}*2  -1

　　}

*/

 

 

#include <cstdio>
int GI(){
  int x=0,c=getchar(),f=0;
  while(c<'0'||c>'9'){if(c=='-')f=1;c=getchar();}
  while(c>='0'&&c<='9')x=x*10+c-'0',c=getchar();
  return f?-x:x;
}
const int maxn=(int)1e7+10;
int p[maxn],cnt;bool flag[maxn];long long ans,phi[maxn];
void init(int n){
    phi[1]=1;
    for(int i=2;i<=n;i++){
        if(!flag[i])p[++cnt]=i,phi[i]=i-1;
        for(int j=1;j<=cnt && i*p[j]<=n;j++){
            flag[i*p[j]]=1;
            if(i%p[j]==0){phi[i*p[j]]=phi[i]*p[j];break;}
            phi[i*p[j]]=phi[i]*(p[j]-1);
        }
    }
    for(int i=2;i<=n;i++)phi[i]+=phi[i-1];
}
int main(){
    int n=GI();
    init(n);
    for(int i=1;i<=cnt;i++)ans+=phi[n/p[i]]*2-1;
    printf("%lld\n",ans);
  return 0;
}