题目链接
思路：
思考一下会发现选择质因子越多的且越小的会使得结果更小，因此预处理前100的质因子，询问直接查询处理数组。需要写大数
ac代码：
import java.util.Scanner;
import java.math.*;
public class Main {public static void main(String[] args) {int N=1000;int pri[]=new int[1005];int vis[]=new int[1005];node ans[]=new node[1005];int cnt=0;int tot=0;for(int i=2;i<=N;i++){if(vis[i]==0) pri[cnt++]=i;for(int j=0;j<cnt&&pri[j]*i<=N;j++){vis[pri[j]*i]=1;if(i%pri[j]==0) continue;}}for(int i=0;i<=1000;i++) {ans[i]=new node();ans[i].p = new BigInteger("0");ans[i].q = new BigInteger("0");ans[i].val = new BigInteger("0");}ans[tot].val=new BigInteger("1");ans[tot].p=new BigInteger("1");ans[tot++].q=new BigInteger("1");for(int i=0;i<=100;i++){ans[tot].val=ans[tot-1].val.multiply(BigInteger.valueOf(pri[i]));ans[tot].p=ans[tot-1].p.multiply(BigInteger.valueOf(pri[i]+1));ans[tot].q=ans[tot-1].q.multiply(BigInteger.valueOf(pri[i]));BigInteger g=ans[tot].p.gcd(ans[tot].q);ans[tot].p=ans[tot].p.divide(g);ans[tot].q=ans[tot].q.divide(g);tot++;}int t;Scanner rd=new Scanner(System.in);t=rd.nextInt();while(t>0){BigInteger n;n=rd.nextBigInteger();for(int i=0;i<tot;i++){
// System.out.print(ans[i].val+"\n"+n+"\n");if(ans[i].val.compareTo(n)==1){System.out.print(ans[i-1].q+"/"+ans[i-1].p+'\n');
// printf("%lld %lld\n",ans[tot].q,ans[tot].p);break;}}t--;}}}
class node{BigInteger p,q,val;
}