Problem:
Problem B: Monday-Saturday Prime Factors

Chief Judge's log, stardate 48642.5.
We have decided to make a problem from elementary number theory.
The problem looks like finding all prime factors of a positive integer,
but it is not.

A positive integer whose remainder divided by 7 is either 1 or 6 is called
a 7N+{1,6} number.
But as it is hard to pronounce,
we shall call it a Monday-Saturday number.

For Monday-Saturday numbers a and b,
we say a is a Monday-Saturday divisor of b
if there exists a Monday-Saturday number x
such that ax = b.
It is easy to show that
for any Monday-Saturday numbers a and b,
it holds that a is
a Monday-Saturday divisor of b
if and only if
a is a divisor of b in the usual sense.

We call a Monday-Saturday number a Monday-Saturday prime
if it is greater than 1 and has no Monday-Saturday divisors
other than itself and 1.
A Monday-Saturday number which is a prime in the usual sense
is a Monday-Saturday prime
but the converse does not always hold.
For example, 27 is a Monday-Saturday prime
although it is not a prime in the usual sense.
We call a Monday-Saturday prime
which is a Monday-Saturday divisor of a Monday-Saturday number a
a Monday-Saturday prime factor of a.
For example, 27 is one of the Monday-Saturday prime factors of 216,
since 27 is a Monday-Saturday prime
and 216 = 27 × 8 holds.

Any Monday-Saturday number greater than 1
can be expressed as a product of one or more Monday-Saturday primes.
The expression is not always unique
even if differences in order are ignored.
For example,

216 = 6 × 6 × 6 = 8 × 27

holds.

Our contestants should write a program that outputs
all Monday-Saturday prime factors
of each input Monday-Saturday number.

Input

The input is a sequence of lines each of which contains a single
Monday-Saturday number.
Each Monday-Saturday number is greater than 1
and less than 300000 (three hundred thousand).
The end of the input is indicated by a line
containing a single digit 1.

Output

For each input Monday-Saturday number,
it should be printed, followed by a colon `:'
and the list of its Monday-Saturday prime factors on a single line.
Monday-Saturday prime factors should be listed in ascending order
and each should be preceded by a space.
All the Monday-Saturday prime factors should be printed only once
even if they divide the input Monday-Saturday number more than once.

Sample Input

205920
262144
262200
279936
299998
1

Output for the Sample Input

205920: 6 8 13 15 20 22 55 99
262144: 8
262200: 6 8 15 20 50 57 69 76 92 190 230 475 575 874 2185
279936: 6 8 27
299998: 299998

Solution in JAVA (judge verdict: Time Limit Exceeded)

import java.util.*;
public class Main {
	Scanner sc;
	LinkedList<Integer> gdlist;
	boolean[] primegd;
	final int max = 3000001;
	
	
	void createGD() {
		primegd = new boolean[max];
		gdlist = new LinkedList<Integer>();
		for(int i=0;i<max;i++) {
			primegd[i] = true;
		}
		for(int i=1;;i++) {
			if(i*7-1>max) break;
			if(primegd[i*7-1]) {
				gdlist.add(i*7-1);
				for(int j=2*(i*7-1);j<max;j+=i*7-1) primegd[j] = false;
			}
			if(primegd[i*7+1]) {
				gdlist.add(i*7+1);
				for(int j=2*(i*7+1);j<max;j+=i*7+1) primegd[j] = false;
			}
		}
		
	}
	
	
	void run() {
		sc = new Scanner(System.in);
		createGD();
		while (true) {
			int n = sc.nextInt();
			if(n == 1) break;
			System.out.print(n + ": ");
			for(Integer it:gdlist) {
				if(n == 1) break;
				if(n % it != 0) continue;
				else {
					System.out.print(it);
//					while(n%it==0) n /= it;
				}
				System.out.print(" ");
			}
			System.out.println();
		}
	}
	public static void main(String[] args) {
		new Main().run();
	}
}