CodeForces 546D （质因子打表法）

Description
Two soldiers are playing a game. At the beginning first of them chooses a positive integer n and gives it to the second soldier. Then the second one tries to make maximum possible number of rounds. Each round consists of choosing a positive integer x > 1, such that n is divisible by x and replacing n with n / x. When n becomes equal to 1 and there is no more possible valid moves the game is over and the score of the second soldier is equal to the number of rounds he performed.

To make the game more interesting, first soldier chooses n of form a! / b! for some positive integer a and b (a ≥ b). Here by k! we denote the factorial of k that is defined as a product of all positive integers not large than k.

What is the maximum possible score of the second soldier?

Input
First line of input consists of single integer t (1 ≤ t ≤ 1 000 000) denoting number of games soldiers play.

Then follow t lines, each contains pair of integers a and b (1 ≤ b ≤ a ≤ 5 000 000) defining the value of n for a game.

Output
For each game output a maximum score that the second soldier can get.

Sample Input
Input
2
3 1
6 3
Output
2
5

**题意：**a！ / b！ 后的数最多能除多少个数才能到 1
问你一个数最多能除多少次的时候就要用上质因子打表了~~~，再求出前缀和

#include <cstdio>#include <cstring>#define M 5000050#define LL long longbool isprime[M];LL num[M];void bymeter(){    memset(num, 0, sizeof(num));    memset(isprime, true, sizeof(isprime));    isprime[1] = false;    for(int i=2; i<M; i++)//质因子打表    {        if(isprime[i])        {            for(int j=i; j<M; j+=i)            {                int temp = j;                while(temp % i == 0)                {                    temp /= i;                    num[j]++;                }                isprime[j] = false;            }        }    }    for(int i=1; i<M; i++)//求前缀和    {        num[i] += num[i-1];    }}int main(){    int t, a, b;    scanf("%d", &t);    bymeter();    while(t--)    {        scanf("%d%d", &a, &b);        printf("%lld\n", num[a] - num[b]);    }    return 0;}