求筛选法欧拉函数 hdu 2824

The Euler function

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2272    Accepted Submission(s): 942

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

#include <iostream>#include <cstdio>#include <cmath>using namespace std;#define N 3000001__int64 phi[N];void init(){    int i, j;    for(i = 1; i < N; i++)        phi[i] = i;    for(i = 2; i < N; i++)        if(i == phi[i]) //若i为素数 第一次不是            for(j = i; j < N; j += i)  //让j累加i                phi[j] = (phi[j] / i) * (i - 1); //求欧拉函数}int main(){    init();    int a, b;    while(scanf("%d%d", &a, &b) != EOF)    {        __int64 ans = 0;        for(int i = a; i <= b; i++)            ans += phi[i];        printf("%I64d\n", ans);    }    return 0;}