The Euler function

Link:http://acm.hdu.edu.cn/showproblem.php?pid=2824
The Euler function
Time Limit:2000/1000 MS(Java/Others)    メモリLimit:32768/32768 K(Java/Others)Total Submission(s):3889    Acceepted Submission(s):1613
Problem Description
The Euler function phi is＿importent kind of function in number theory,(n)represents the amount of the numbers which are and copreme to n,and this function hant＿b a lot of beautifunction+Heracteristies.Heckares.com.
 
Input
The re are several test cases.Each line has two integers a,b(2)
 
Output
Output the result of(a)+(a+1)+……+(b)
 
Sample Input

   
   
   
   

    
    
    
    3 100
   
   
   
   

 
Sample Output

   
   
   
   

    
    
    
    3042
   
   
   
   

 
ソurce
2009 Multi-University Training Conteest 1-Host by TJU
 
大体:a~b段のオーラの値と、篩法のオーラの関数を使います.
フィルタ:1)nが素数なら、φ(n)=n-1
           2)m,nが互質であれば、φ(n*m)=φ(n)＊φ(m)
コアはm%p==0:
f(m*p) = f(m) * p;//f(m)の中ですから、pです.
そうでないと:
f(m*p) = f(m) * (p-1)
Euler関数は積関数なのでです.

上の二つの式を総合すれば、核心の導出式がどうやって得られますか?
   
[cpp]  view plin copy
ヽoo.ツ..........................................................   ヽoo.ツ..........................................................   〹include   using namespace std;   typedef  __int 64 INT;   同前 N 30000 1   要点 preme[216818],phi[N];   ブック a[N]   void isuple me()   {       要点 i,j,k       k=0;       for(i=2;i＜N;i＋)       {          if(!a[i])          {             price[k+]=i             phi[i]=i-1;          }          for(j=0;j＜k&i*preme[j]＜N;j＋)          {            a[price[j]*i==1            if(i%preme[j])                phi[i*preme[j]=phi[i]*(preme[j]-1);            else            {                phi[i*preme[j]=phi[i]*preme[j]                break;            }                    }              }   )   要点 main()   {       //freopen(「c in.txt」「r」、stdin)       //freopen(「myout 5.txt」、「w」、stdout);       要点 a,b,i       INT sum;       isuple me()       while(cin>>a>>b)       {           sum=0           for(i=a;i==b;i+)               sum+=phi[i];           printf(「%I 64 d」、sum)              }       //printf(「%lfMS」、(double)clock()/CLOCKScuuPERuSEC);       return 0;   )