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: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;

import static java.lang.Integer.parseInt;

/**
 * Monday-Saturday Prime Factors
 */
public class Main {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line;

		boolean[] ns = new boolean[300000];
		for (int i = 0; ; i++) {
			int m = i * 7 + 1;
			int s = i * 7 + 6;
			if (m < ns.length) ns[m] = true;
			else break;
			if (s < ns.length) ns[s] = true;
			else break;
		}
		ns[1] = false;
		//System.out.println(ns[299998]);

		for (int i = 6; i < ns.length; i++) {
			if (ns[i]) {
				for (int j = 2; j < ns.length / i; j++) {
					ns[i * j] = false;
				}
			}
		}

		List<Integer> ps = new ArrayList<>();
		for (int i = 0; i < ns.length; i++) {
			if (ns[i]) ps.add(i);
		}

		while ((line = br.readLine()) != null && !line.isEmpty()) {

			int n = parseInt(line);
			if (n == 1) break;

			StringBuilder sb = new StringBuilder();
			sb.append(n + ":");

			for (int i : ps) {
				if (n % i == 0) sb.append(" " + i);
			}
			System.out.println(sb.toString());

		}//end while
	}//end main
}