1到n里面素数的个数n<=1e11

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2016沈阳网络赛的最后一题，记录一下这个模板，来自某某大神，并不懂这个的原理，先放着当模板。

////Created by just_sort 2016/9/12 17:01//Copyright (c) 2016 just_sort.All Rights Reserved//#include <set>#include <map>#include <queue>#include <stack>#include <cmath>#include <cstdio>#include <cstdlib>#include <cstring>#include <iostream>#include <algorithm>using namespace std;#define ll long longll f[340000],g[340000],n;void init(){    ll i,j,m;    for(m=1; m*m<=n; ++m)f[m]=n/m-1;    for(i=1; i<=m; ++i)g[i]=i-1;    for(i=2; i<=m; ++i)    {        if(g[i]==g[i-1])continue;        ll x=min(m-1,n/i/i);        for(j=1; j<=x; ++j)        {            if(i*j<m)f[j]-=f[i*j]-g[i-1];            else f[j]-=g[n/i/j]-g[i-1];        }        x=i*i;        for(j=m; j>=x; --j)g[j]-=g[j/i]-g[i-1];    }}int main(){    while(scanf("%I64d",&n)!=EOF)    {        init();        printf("%I64d\n",f[1]);    }    return 0;}

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