The Euler function

题目描述：

Problem Description

The Euler function phi is an important kind of function in number theory, (n) represents the amount of the numbers which are smaller than n and coprime to n, and this function has a lot of beautiful characteristics. Here comes a very easy question: suppose you are given a, b, try to calculate (a)+ (a+1)+....+ (b)

Input

There are several test cases. Each line has two integers a, b (2<a<b<3000000).

Output

Output the result of (a)+ (a+1)+....+ (b)

Sample Input

3 100

Sample Output

3042

思路：就是求一个区间内的欧拉函数之和，

给出一个结论：

 设E( x)为X的欧拉函数，p为质数

对于E（x*p）  

if   p是x的因数  E(x*p)=E(x)*p;

else  E (x*P)=E(x)*(p-1);

代码：

#include<bits/stdc++.h>
using namespace std;
const int maxv=3e6+10;
int v[3000005],a[3000006],b[3000005];//b数组就是欧拉函数
void init(){
	for(int i=2;i<3000006;i++){
		if(!v[i]){
			a[++a[0]]=i;
			b[i]=i-1; 
		}
		for(int j=1;j<=a[0]&&i*a[j]<3000006;j++){
			v[i*a[j]]=1;
			if(i%a[j]==0){
				b[i*a[j]]=b[i]*a[j];
				break;
			}else{
				b[i*a[j]]=b[i]*(a[j]-1);
			}
		}
	}
} 
int main(){
	int n,m,len;
	init();
	long long sum=0;
	cin>>n>>m;
	if(n>m)swap(n,m);
	for(int i=n;i<=m;i++)sum+=b[i];
	cout<<sum;
	
}