divisors

euler.py

def generate_primes(n):
  seive = [True] * n
  pr = []
  for i in range(2, n):
    if seive[i]:
      j = 2 * i
      while j < n:
        seive[j] = False
        j += i
      pr.append(i)
  return pr


primes = generate_primes(1000)
fact = [[0 for x in range(1000)] for y in range(1000)]


def power_in_factorial(p, n):
  """Return the exponent of the prime p in the factorization of n!"""
  result = 0
  while True:
    n //= p
    if not n:
      break
    result += n
  return result


def count_factorial(n):
  dic = {}
  for prime in primes:
    if prime > n: break
    dic[prime] = power_in_factorial(prime, n)
  return dic


n, k = 6, 3


def diff(a, b):
  for key in b:
    a[key] -= b[key]
  return a


def get(dic):
  val = 1
  for key in dic:
    val *= (dic[key] + 1)
  return val


def choose(n):
  cc = [[0 for x in range(n + 1)] for y in range(n + 1)]
  for i in range(1, n):
    for j in range(1, i + 1):
      a, b, c, = count_factorial(i), count_factorial(j), count_factorial(i - j)
      a = diff(a, b)
      a = diff(a, c)
      ans = get(a)
      cc[i][j] = ans
  return cc


c = choose(435)

for i in range(434):
  for j in range(i + 1):
    print("{} ".format(c[i][j]), end = "")
  print()