HDU 2824 The Euler function

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

 

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线性筛求欧拉函数~

用到的性质是：

（1）当p是质数时，φ（p）=p-1；

（2）如果i%p==0，那么φ（i*p）=p*φ（i）.

然后，输入是多组数据……

#include<cstdio>int x,y,a[3000001],phi[3000001];long long tot;bool b[3000001];void findd(int u){phi[1]=1;for(int i=2;i<=u;i++){if(!b[i]){a[++a[0]]=i;phi[i]=i-1;}for(int j=1;j<=a[0];j++){if(a[j]*i>u) break;b[a[j]*i]=1;if(i%a[j]==0){phi[a[j]*i]=phi[i]*a[j];break;}phi[a[j]*i]=phi[i]*(a[j]-1);}}}int main(){findd(3000000);while(scanf("%d%d",&x,&y)==2){tot=0;for(int i=x;i<=y;i++) tot+=(long long)phi[i];printf("%lld\n",tot);}return 0;}