51nod1239 欧拉函数之和

参考陈牧歌在apio2018的讲课课件

#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
typedef long long ll;
ll n;
int pri[4641590], cnt, phi[4641590], msh[1544665][2];
bool isp[4641590];
const int mod=1000000007;
int getHash(ll x){
	int p=x%1544657;
	while(msh[p][0] && msh[p][0]!=x)	p = (p + 1) % 1544657;
	return p;
}
int getPhi(ll x){
	if(x<=4641581)	return phi[x];
	int p=getHash(x);
	if(msh[p][0])	return msh[p][1];
	msh[p][0] = x;
	ll lst, re=0;
	for(ll i=2; i<=x; i=lst+1){
		lst = x / (x / i);
		ll tmp=(ll)getPhi(x/i) * (lst-i+1) % mod;
		re = (re + tmp) % mod;
	}
	x %= mod;
	re = ((ll)x * (x + 1) % mod * 500000004 % mod - re + mod) % mod;
	msh[p][1] = re;
	return re;
}
int main(){
	memset(isp, true, sizeof(isp));
	isp[0] = isp[1] = false;
	phi[1] = 1;
	for(int i=2; i<=4641581; i++){
		if(isp[i])	pri[++cnt] = i, phi[i] = i - 1;
		for(int j=1; j<=cnt && i*pri[j]<=4641581; j++){
			isp[i*pri[j]] = false;
			if(i%pri[j]==0){
				phi[i*pri[j]] = phi[i] * pri[j];
				break;
			}
			else	phi[i*pri[j]] = phi[i] * (pri[j] - 1);
		}
	}
	for(int i=2; i<=4641581; i++)
		phi[i] = (phi[i-1] + phi[i]) % mod;
	cin>>n;
	cout<<getPhi(n)<<endl;
	return 0;
}