Mathematics: Euler function Review

Konjac is really too residue of ...... especially math portion abuse many chiefs residue left ......

So today I work hard konjac decision charged the math! Review the Euler function first ...... / paste face / paste face

Euler function definition: 1 ~ N N and the number of prime numbers is called the Euler function, referred to as φ (N).

Euler function general formula: φ (N) =

Proof: Let p be prime factors N, multiples of 1 ~ N in a total of N p / p number,

　　Similarly, if N q is the quality factor, N is a multiple of q 1 ~ N are / q th.

　　If we / p and N / N to remove this number q, where q is a common multiple of p is excluded twice, to add back.

　　Therefore, the number of 1 ~ N in number N does not contain a common prime factors p or q is: N * (1-1 / p) (1-1 / q)

　　(More than prove that uses the inclusion-exclusion principle)

　　QED.

Road to the template title

题目大意：给出一段区间，求出这段区间的所有数的欧拉函数值和。


Out-board problem. Do not explain, on the code!

 

 

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
int phi[3000003];
int main()
{
    int a,b;
    long long ans=0;
    while(scanf("%d %d",&a,&b)!=EOF)
    {
        ans=0;
        for(int i=2;i<=b;++i)
            phi[i]=i;
        for(int i=2;i<=b;++i)
            if(phi[i]==i)
                for(int j=i;j<=b;j+=i)
                    phi[j]=phi[j]/i*(i-1);
        for(int i=a;i<=b;++i)
            ans+=(long long)phi[i];
        printf("%lld\n",ans);
    }
    return 0;
}