HDU 2824 The Euler function（欧拉函数）

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

 

题意：

给两个数a和b，求这两个数之间的数的欧拉函数值之和

 

思路：

利用欧拉函数和它本身不同质因数的关系，用筛法计算出某个范围内所有数的欧拉函数值。

（p是数N的质因数）

 

代码：

#include<cstdio>
#include<iostream>
#include<algorithm>
using namespace std;
#define LL long long
#define max 3000010
LL la[max];
void eular()
{
	int i,j;
	la[1]=0;
	for(i=2;i<max;++i)
		la[i]=i;
	for(i=2;i<max;++i)
	{
		if(la[i]==i)
		{
			for(j=i;j<max;j=j+i)
				la[j]=la[j]/i*(i-1);
		}
	}
	for(i=2;i<max;++i)
		la[i]=la[i]+la[i-1];
}

int main()
{
	eular();
    int a,b;
    LL sum=0;
    while(~scanf("%d%d",&a,&b))
    {
	    int i,j;
		sum=la[b]-la[a-1];
		printf("%lld\n",sum);
	}
}

 

来源：CSDN

作者：淼润淽涵

链接：https://blog.csdn.net/wcxyky/article/details/103976632