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: WA: Presentation Error)

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

int not_mon_sat_prime[3000001];//initialized to zero

int is_mon_sat(int num)
{
    if(num % 7 == 1 || num % 7 == 6){
        return 1;
    }else{
        return 0;
    }
}


int next_mon_sat(int num)
{
    num++;
    for(; !is_mon_sat(num); num++) ;

    return num;
}

void mon_sat_prime(int num)
{
    int i;
    int limit = sqrt(num);

    not_mon_sat_prime[1] = 1;

    for(i = 2; i <= num; i++){//mon_sat number is 0 others are 1
        if(!is_mon_sat(i)){
            not_mon_sat_prime[i] = 1;
        }
    }

    for(i = 6; i <= limit; i = next_mon_sat(i)){
        int j;
        for(j = 2; j <= num / i; j++){
            not_mon_sat_prime[i * j] = 1;//not a mon_sat_prime number
        }
    }

}

int main(void)
{
    mon_sat_prime(3000000);

    while(1){
        int num;
        int i;

        scanf("%d", &num);

        if(num == 1)
            break;

        printf("%d: ", num);

        for(i = 1; i <= num; i++){
            if(!not_mon_sat_prime[i] && num % i == 0){
                printf("%d ", i);
            }
        }

        printf("\n");
    }

    return 0;
}