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 <stdio.h>


#define MAX_PRIME	(300100)

int prime[MAX_PRIME + 1];

void make_prime(void)
{
    int i;
    int j;
    int n;
    int c;
    
    for (i = 1; i <= MAX_PRIME / 7; i++){
        if (prime[i * 7 - 1] == 0){
            for (j = (i * 7 - 1) * 2; j <= MAX_PRIME; j += (i * 7 - 1)){
				prime[j] = 1;
//printf("<%d>", j);
            }
        }
        if (prime[i * 7 + 1] == 0){
            for (j = (i * 7 + 1) * 2; j <= MAX_PRIME; j += (i * 7 + 1)){
				prime[j] = 1;
//printf("[%d]", j);
            }
        }
    }
}


int main(void)
{
    int n;
    int i;
    
    make_prime();
#if 0
for (i = 7; i <= 300100; i += 7){
    if (prime[i - 1] == 0){
        printf(" %d", i - 1);
    }
    if (prime[i + 1] == 0){
        printf(" %d", i + 1);
    }
}
#endif
    while (1){
        scanf("%d", &n);
        if (n == 1){
            break;
        }
        
        printf("%d:", n);
        
        i = 7;
        while (n >= i - 1){
            if (prime[i - 1] == 0){
                if (n % (i - 1) == 0){
                    printf(" %d", i - 1);
                }
            }
            if (prime[i + 1] == 0){
                if (n % (i + 1) == 0){
                    printf(" %d", i + 1);
                }
            }
            i += 7;
        }
        printf("\n");
    }
    return (0);
}