概率DP

比較精妙。

import java.util.*;
import java.io.*;
public class Main {
	static boolean isPrimer[];
	static int l=0;
	static int len=1000010;
	static int primer[];
	static StreamTokenizer in=new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
	static double find[];
	public static void main(String[] args) throws Exception{
		int t=getInt();
		isPrimer=new boolean[len];
		primer=new int[len];
		find=new double[len];
		for(int i=2;i<len;i++)
			if(!isPrimer[i])
				for(int j=2;i*j<len;j++)
					isPrimer[i*j]=true;
		for(int i=2;i<len;i++) {
			if(!isPrimer[i])
				primer[l++]=i;
		}
		for(int c=1;c<=t;c++) {
			int n=getInt();
			double ans=dfs(n);
			//System.out.print("Case #"+c+": ");
			System.out.printf("Case %d: %.10f",c,ans);
			System.out.println();
		}
			
	}
	static double dfs(int n) {
		if(n==1)return 0;
		if(find[n]!=0)return find[n];
		double ans=0;
		int g=0,p=0;
		for(int i=0;i<l&&primer[i]<=n;i++) {
			p++;
			if(n%primer[i]==0) {
				g++;
				ans+=dfs(n/primer[i]);
			}
		}
		//System.out.println(n+" "+g);
		find[n]=(ans+p)/g;
		return find[n];
	}
	public static double getDouble() throws Exception {
		in.nextToken();
		return in.nval;
	}
	public static int getInt() throws Exception{
		in.nextToken();
		return (int)in.nval;
	}
}