old_contents: """
  Highly divisible triangular numbers
  Problem 12
  The sequence of triangle numbers is generated by adding the natural numbers. So
  the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten
  terms would be:
  
  1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
  
  Let us list the factors of the first seven triangle numbers:
  
   1: 1
   3: 1,3
   6: 1,2,3,6
  10: 1,2,5,10
  15: 1,3,5,15
  21: 1,3,7,21
  28: 1,2,4,7,14,28
  We can see that 28 is the first triangle number to have over five divisors.
  
  What is the value of the first triangle number to have over five hundred
  divisors?
  """
  from math import sqrt
  
  
  def count_divisors(n):
      nDivisors = 0
      for i in range(1, int(sqrt(n)) + 1):
          if n % i == 0:
              nDivisors += 2
      # check if n is perfect square
      if n ** 0.5 == int(n ** 0.5):
          nDivisors -= 1
      return nDivisors
  
  
  def solution():
      """Returns the value of the first triangle number to have over five hundred
      divisors.
  
      # The code below has been commented due to slow execution affecting Travis.
      # >>> solution()
      # 76576500
      """
      tNum = 1
      i = 1
  
      while True:
          i += 1
          tNum += i
  
          if count_divisors(tNum) > 500:
              break
  
      return tNum
  
  
  if __name__ == "__main__":
      print(solution())
  
new_contents: """
  Highly divisible triangular numbers
  Problem 12
  The sequence of triangle numbers is generated by adding the natural numbers. So
  the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten
  terms would be:
  
  1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
  
  Let us list the factors of the first seven triangle numbers:
  
   1: 1
   3: 1,3
   6: 1,2,3,6
  10: 1,2,5,10
  15: 1,3,5,15
  21: 1,3,7,21
  28: 1,2,4,7,14,28
  We can see that 28 is the first triangle number to have over five divisors.
  
  What is the value of the first triangle number to have over five hundred
  divisors?
  """
  
  
  def count_divisors(n):
      nDivisors = 1
      i = 2
      while i * i <= n:
          multiplicity = 0
          while n % i == 0:
              n //= i
              multiplicity += 1
          nDivisors *= multiplicity + 1
          i += 1
      if n > 1:
          nDivisors *= 2
      return nDivisors
  
  
  def solution():
      """Returns the value of the first triangle number to have over five hundred
      divisors.
  
      >>> solution()
      76576500
      """
      tNum = 1
      i = 1
  
      while True:
          i += 1
          tNum += i
  
          if count_divisors(tNum) > 500:
              break
  
      return tNum
  
  
  if __name__ == "__main__":
      print(solution())
  
subject: Improve Project Euler problem 012 solution 1 (#5731)