from itertools import product, zip_longest

def split(arr,mults): #traverses the possibility tree
  if arr == []: #if the list of divisors (arr) is exhausted
    return int(all(x >= 0 for x in mults)) #return whether an integer is made
  plus = [p+q for p,q in zip_longest(mults,arr[0],fillvalue = 0)]
  minus = [p-q for p,q in zip_longest(mults,arr[0],fillvalue = 0)]
  return split(arr[1:],plus)+split(arr[1:],minus)

def facs(arr): #generates prime signatures of divisors, given prime signature
  powers = [[j for j in range(i+1)] for i in arr]
  res = list(product(*powers))
  res.pop(0) #removes 1
  return res

def multiparts(n,mx): #returns multiplicative partitions
  if n == 1: return [[]]
  res = []
  for i in range(2,min(mx,n)+1):
    if n%i: continue
    for j in multiparts(n//i,i):
      res.append([i-1] + j)
  return res

res = []
for n in range(1,21): #for tau ranging from 1 to 20
  for num in multiparts(n,n): #iterate over potential prime signatures
    res.append(split(facs(num),[]))
print(sorted((res)))