HDU——T 2824 The Euler function

Posted 2020-10-01

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

 1 #include <algorithm>
 2 #include <cstdio>
 3 
 4 using namespace std;
 5 
 6 #define LL long long
 7 const int N(3000233);
 8 LL a,b,phi[N];
 9 
10 void All_phi()
11 {
12     for(int i=1;i<=N;i++)
13       phi[i]=i;
14     for(int i=2;i<=N;i++)
15       if(phi[i]==i)
16         for(int j=i;j<=N;j+=i)
17           phi[j]=phi[j]/i*(i-1);
18 }
19 
20 int main()
21 {
22     All_phi();
23     for(int i=1;i<=N+1;i++) phi[i]=phi[i-1]+phi[i];
24     for(;scanf("%d%d",&a,&b)!=EOF;)
25         printf("%I64d\n",phi[b]-phi[a-1]);
26     return 0;
27 }