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Problem Description
A positive proper divisor is a positive divisor of a number n, excluding n itself. For example, 1, 2, and 3 are positive proper divisors of 6, but 6 itself is not.
Peter has two positive integers n and d. He would like to know the number of integers below n whose maximum positive proper divisor is d.
Input
There are multiple test cases. The first line of input contains an integer T (1≤T≤106), indicating the number of test cases. For each test case:
The first line contains two integers n and d (2≤n,d≤109).
Output
For each test case, output an integer denoting the answer.
Sample Input
9
10 2
10 3
10 4
10 5
10 6
10 7
10 8
10 9
100 13
Sample Output
1
2
1
0
0
0
0
0
4
Source
BestCoder Round #84
思路,要想找1到n里最大因子是d的个数,可以变换一下式子,d<dx<n,这样就变成了求满足条件的x的个数,同时dx还必须满足d是它的最大因子,那么我们可以设d的最小素因子为y,答案就一定是【2,min((n-1)/d,m)】区间的素数个数,素数打表就好了。
#include<bits/stdc++.h>using namespace std;#define ll long longconst int maxn=5e5+100;int n,d,prime[maxn],top=0,pos[maxn],isprime[maxn]={ 0};void Prime(int n){ for(int i=2;i<=n;++i) { if(!isprime[i]) prime[++top]=i,pos[i]=pos[i-1]+1; else pos[i]=pos[i-1]; for(int j=1;j<=top;++j) { if(i*prime[j]>n) break; isprime[i*prime[j]]=1; if(i%prime[j]==0) break; } }}int main(){ int T; Prime(maxn); scanf("%d",&T); while(T--) { scanf("%d %d",&n,&d); if(d>=(n+1)/2){ printf("0\n");continue; } int temp=(n-1)/d,flag=0; for(int j=1;j<=top&&prime[j]*prime[j]<=d;++j) { if(d%prime[j]==0) { flag=1; temp=min(temp,prime[j]); break; } } if(!flag) temp=min(temp,d); printf("%d\n",pos[temp]); }}
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