[杜教筛模板] 51Nod 1239 欧拉函数之和

模板题



#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include <tr1/unordered_map>
typedef long long ll;
using namespace std;
using namespace std::tr1;

const int maxn=10000000;

int prime[1000000],num;
int vst[maxn+5],phi[maxn+5];

const int P=1e9+7;
const int inv=500000004;

inline void Pre(){
phi[1]=1;
for (int i=2;i<=maxn;i++){
if (!vst[i]) prime[++num]=i,phi[i]=i-1;
for (int j=1;j<=num && (ll)i*prime[j]<=maxn;j++){
vst[i*prime[j]]=1;
if (i%prime[j]==0){
phi[i*prime[j]]=phi[i]*prime[j];
break;
}else
phi[i*prime[j]]=phi[i]*phi[prime[j]];
}
}
for (int i=1;i<=maxn;i++) (phi[i]+=phi[i-1])%=P;
}

unordered_map<ll,int> S;

inline int Sum(ll n){
if (n<=maxn) return phi
;
if (S.find(n)!=S.end()) return S
;
int tem=(ll)(n%P)*((n+1)%P)%P*inv%P; ll l,r;
for (l=2;l*l<=n;l++) (tem+=P-Sum(n/l))%=P;
for (ll t=n/l;l<=n;l=r+1,t--)
r=n/t,(tem+=P-(ll)(r-l+1)*Sum(t)%P)%=P;
return S
=tem;
}

int main(){
ll n;
freopen("t.in","r",stdin);
freopen("t.out","w",stdout);
Pre();
scanf("%lld",&n);
printf("%d\n",Sum(n));
return 0;
}