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: Accepted)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) throws java.io.IOException {
        final int MAX = 300000;
        Scanner sc = new Scanner(System.in);
        boolean[] msprime = new boolean[MAX + 1];
        int limit = MAX / 7;
        for (int i = 0; i <= limit; i++) {
            if ((7 * i + 1) > MAX)
                break;
            msprime[7 * i + 1] = true;
            if ((7 * i + 6) > MAX)
                break;
            msprime[7 * i + 6] = true;
        }
        msprime[1] = false;

        for (int i = 0; i < MAX + 1; i++) {
            if (msprime[i]) {
                if(i*6>MAX)continue;
                msprime[i * 6] = false;
                for (int j = 1; j <= limit; j++) {
                    if (i * (7 * j + 1) > MAX)
                        break;
                    msprime[i * (7 * j + 1)] = false;
                    if (i * (7 * j + 6) > MAX)
                        break;
                    msprime[i * (7 * j + 6)] = false;
                }
            }
        }
       // System.out.println(Arrays.toString(msprime));
        while (true) {
            int n = sc.nextInt();
            if (n == 1)
                break;
            System.out.print(n + ":");
            if(6>n)continue;
            if (n % 6 == 0)
                System.out.print(" 6");
            for (int i = 1; i<= n; i++) {
                if((7*i+1)>n)break;
                if (msprime[7 * i + 1] && n % (7 * i + 1) == 0)
                    System.out.print(" " + (7 * i + 1));
                if((7*i+6)>n)break;
                if (msprime[7 * i + 6] && n % (7 * i + 6) == 0)
                    System.out.print(" " + (7 * i + 6));
            }
            System.out.println();
        }
    }
}