output_description: 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.
input_description: 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.
attempt: this_prime_num = [0 for i in range(300001)]
  
  for i in range(300001):
      if i % 7 == 1 or i % 7 == 6:
          this_prime_num[i] = 1
  for i in range(2, 300001):
      j = i * 2
      while this_prime_num[i] == 1 and j < len(this_prime_num):
          # print(j)
          this_prime_num[j] = 0
          j += i
  
  
  this_primenum_list = []
  for i in range(2, len(this_prime_num)):
      if this_prime_num[i]:
          this_primenum_list.append(i)
  print(this_primenum_list[:30])
  ans_list = []
  while True:
      n = int(input())
      if n == 1:
          break
      i = 0
      ans = [n]
      while this_primenum_list[i] <= n:
          # print(i)
          if n % this_primenum_list[i] == 0:
              ans.append(this_primenum_list[i])
          i += 1
          if i >= len(this_primenum_list):
              break
      ans_list.append(ans)
  
  for i in ans_list:
      print(str(i[0]) + ":", end="")
      for j in i[1:]:
          print("", end=" ")
          print(j, end="")
      print()
  
problem_description: 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
  7** _N_** +{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 _a_ _x_
  = _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.
samples: [{"input": "262144\n    262200\n    279936\n    299998\n    1", "output": ": 6 8 13 15 20 22 55 99\n    262144: 8\n    262200: 6 8 15 20 50 57 69 76 92 190 230 475 575 874 2185\n    279936: 6 8 27\n    299998: 299998"}]