URAL 2070 Interesting Numbers （素数枚举）

大体题意：

两个人，一个人认为一个数如果是素数的话，那么是符合要求的，另外一个人认为这个数的因子个数是素数的话，那么才是符合要求的！

给你一个区间 [L，R]，求出该区间内 同时符合两个人要求 或者同时不符合两人要求数的个数!

思路：

很有意思的一道题目！

我们可以用间接法来求， 总数肯定是R-L + 1 可以求出符合一个但不符合另一个人数的个数 ！

我们很容易想到  如果这个数是素数的话，那么他肯定是符合要求的！

接下来，问题就转换成了  求L到R区间内 有多少个数是合数并且这个数的因子个数是素数！

求这个问题，我们就要考虑这个数的素因子了！

假设这个数是p1^a * p2^b * p3 *c ......

如果素因子不止一个的话，那么他的因子个数是(a+1) * (b+1) * (c+1) 这肯定不是素数，首先就有三个因子！

因此素因子必须只有一个！

假设是p ^ n  我们只需要看看n 是不是素数即可!  n肯定是很小的！

题目区间限制是10^12，  开方得 10^6  我们只需要枚举1 ~ 10^6内的素数即可！

注意这里的n 要大于1 ，否则他就是素数了！

注意 这是闭区间 ，wa了好几次！

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<vector>
using namespace std;
const int maxn = 1000000 + 10;
const int inf = 0x3f3f3f3f;
typedef long long ll;
vector<ll>prime;
int len_pri;
int vis[maxn];
void init(){
int len = sqrt(maxn) + 1;
for (int i = 2; i <= len; ++i)if (!vis[i])
for (int j = i*i; j <= maxn; j += i)vis[j] = 1;
for (int i = 2; i <= maxn; ++i)if (!vis[i])prime.push_back(i);
len_pri = (int)prime.size();
}
int main(){
init();
ll l,r;
scanf("%I64d %I64d",&l,&r);
ll ans = 0ll;
for (int i = 0; i < len_pri; ++i){
ll cur = 1ll;
if (prime[i] * prime[i] > r)break;
int sum = 0;
while(cur < l)cur *= prime[i],++sum;
while(cur <= r){
if (sum > 1 && !vis[sum+1])++ans;
cur *= prime[i];
++sum;
}
}
printf("%I64d\n",r-l+1ll-ans);
return 0;
}

2070. Interesting Numbers

Time limit: 2.0 second

Memory limit: 64 MB

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 ≤ 1012).

Output

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

Samples

input	output
3 7	4
2 2	1
77 1010	924

Problem Author: Alexey Danilyuk
Problem Source: Ural Regional School Programming Contest 2015

Tags: number theory  (

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