HDU 2824 The Euler function

The Euler function

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 3789    Accepted Submission(s): 1569

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

 

 

线性筛选欧拉函数

 

#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <iostream>
using namespace std;
const int N = 3000010;
long long  phi[N];
void solve()
{
    memset( phi , 0 ,sizeof phi );
    phi[1] = 1 ;
    for( int i = 2 ; i < N ; ++i ){
        if( !phi[i] ){
            for( int j = i ; j < N ; j += i ){
                if( !phi[j] ) phi[j] = j ;
                phi[j] = phi[j] / i * ( i - 1 );
            }
        }
    }
}

int main()
{
    ios::sync_with_stdio(false);
    solve();
    for( int i = 2 ; i < N ; ++i ){
        phi[i] += phi[i-1] ;
    }
    int a , b ;
    while( cin >> a >> b  ){
        cout << phi[b] - phi[ a - 1 ] <<endl;
    }
}