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++14 (judge verdict: Accepted)

#include <iostream>
#include <string>
#include <cstring>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <queue>

#define FOR(i, f, n) for(int (i) = (f); (i) < (n); (i)++)
#define RFOR(i, f, n) for(int (i) = (f); (i) >= (n); (i)--)
#define REP(i, n) for(int (i) = 0; (i) < (n); (i)++)
#define RREP(i, n) for(int (i) = (n); (i) >= 0; (i)--)
#define rep(i, n) for(int (i) = 0; (i) < (n); (i)++)
#define rrep(i, n) for(int (i) = (n); (i) >= 0; (i)++)
#define p(...) printf(__VA_ARGS__); cout << endl;
#define input(x) x; cin >> x;
#define list_input(x, n) x[(n)]; for(int (i) = 0; (i) < (n); (i)++) cin >> x[i];
#define lambda(a, b, c) [](const a, const b){ return c ;}
#define key(t, x, compare) [](const t& a, const t& b){ return a x compare b x ;}

using namespace std;

using pii = pair<int, int>;

int maina(){
  int input(n);
  if(n == 1) return false;
  vector<int> a;
  FOR(i, 6, pow(n, 0.5) + 1){
    if(n%i == 0 && (i%7 == 1 || i%7 == 6)){
      a.push_back(i);
      a.push_back(n/i);
    }
  }

  vector<int> result;
  bool flg = true;
  cout << n << ":";
  for(int i: a){
    for(int j: a){
      if(i != j && i % j == 0){
        goto ELSE;
      }
    }
    for(auto k: result){
      if(k == i) goto ELSE;
    }
    result.push_back(i);
    flg = false;
ELSE:
    {}
  }
  sort(result.begin(), result.end());
  for(int i: result) printf(" %d", i);
  if(flg) cout << " " << n;
  cout << endl;
  return true;
}

int main(){
  while(maina());
}