HDU——T 2824 The Euler function

http://acm.hdu.edu.cn/showproblem.php?pid=2824

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 7752    Accepted Submission(s): 3217

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

 

Source

2009 Multi-University Training Contest 1 - Host by TJU

 

 

欧拉函数表。前缀和

#include <algorithm>
#include <cstdio>

using namespace std;

#define LL long long
const int N(3000233);
LL a,b,phi[N];

void All_phi()
{
    for(int i=1;i<=N;i++)
      phi[i]=i;
    for(int i=2;i<=N;i++)
      if(phi[i]==i)
        for(int j=i;j<=N;j+=i)
          phi[j]=phi[j]/i*(i-1);
}

int main()
{
    All_phi();
    for(int i=1;i<=N+1;i++) phi[i]=phi[i-1]+phi[i];
    for(;scanf("%d%d",&a,&b)!=EOF;)
        printf("%I64d
",phi[b]-phi[a-1]);
    return 0;
}