URAL 2070 Interesting Numbers

Discription

Nikolay and Asya investigate integers together in their spare time. Nikolay thinks an integer is interesting if it is a prime number. However, Asya thinks an integer is interesting if the amount of its positive divisors is a prime number (e.g., number 1 has one divisor and number 10 has four divisors).

Nikolay and Asya are happy when their tastes about some integer are common. On the other hand, they are really upset when their tastes differ. They call an integer satisfying if they both consider or do not consider this integer to be interesting. Nikolay and Asya are going to investigate numbers from segment [ L; R] this weekend. So they ask you to calculate the number of satisfying integers from this segment.

Input

In the only line there are two integers L and R (2 ≤ L ≤ R ≤ 10 ¹²).

Output

In the only line output one integer — the number of satisfying integers from segment [ L; R].

Example

input	output
3 7	4
2 2	1
77 1010	924

 

 

    尝试用区间内总数减去不满足条件的数个数来得到答案。

    不满足的数有两种:是质数但是约数个数不是质数，不是质数但是约数个数是质数。

    第一种情况不存在，而第二种情况又得满足它是某个质数的若干次方，所以这就是一个水题了23333

 

 

#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int maxn=1000000;
int zs[maxn/5],t=0;
bool v[maxn+5];
ll L,R;

inline void init(){
	v[1]=1;
	for(int i=2;i<=maxn;i++){
		if(!v[i]) zs[++t]=i;
		for(int j=1,u;j<=t&&(u=zs[j]*i)<=maxn;j++){
			v[u]=1;
			if(!(i%zs[j])) break;
		}
	}
}

inline ll solve(ll x){
	ll ans=0;
	
	for(int i=2;i*(ll)i<=x;i++) if(!v[i])
		for(ll j=i*(ll)i,u=2;j<=x;j=j*(ll)i,u++) if(!v[u+1]) ans++;
	
	return x-ans;
} 

int main(){
	init();
	cin>>L>>R;
	printf("%lld\n",solve(R)-solve(L-1));
	return 0;
}