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 C++ (judge verdict: Accepted)

#include <cstdio>
#include <iostream>
#include <cmath>
#include <ctype.h>
#include <string> 
#include <sstream>
#include <iostream>
#include <algorithm>
#include <cstdlib>
#include <map>
#include <queue>
#include <utility>
#include <vector>
#include <set>
 
using namespace std;

bool isprime(int n);
 
int main()
{
   int n;
   while(1){
    cin >> n;
    if(n == 1) break;
    cout << n << ':';
    for(int i = 0; i <= n / 7; i++){
        int divisor = 0;
        if(n % (7 * i + 1) == 0){
            divisor = 7 * i + 1;
            if(isprime(divisor)) cout << ' ' << divisor;
        } 
        if(n % (7 * i + 6) == 0){
            divisor = 7 * i + 6;
            if(isprime(divisor)) cout << ' ' << divisor;
        } 
    }
        cout << endl;
    }
    return 0;
}

bool isprime(int n)
{
    if(n == 1) return false;
    else if(n == 6) return true;
    else if(n % 6 == 0) return false;
    else {
        for(int i = 1; 7 * i <= n; i++){
            if(n == 7 * i + 1) break;
            else if(n == 7 * i + 6){
                if(n % (7 * i + 1) == 0) return false;
                else return true;
            } else if(n % (7 * i + 1) == 0 || n % (7 * i + 6) == 0) return false;
        }
    }
    return true;
}