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