





"""simple docstring"""
import math

def 		_SCREAMING_SNAKE_CASE (_UpperCAmelCase				:						int ):
 if not isinstance(lowercase__     ,    lowercase__ ):
  lowerCAmelCase													=   F'Input value of [number={number}] must be an integer'
  raise TypeError(lowercase__ )
 if number < 1:
  lowerCAmelCase													=   F'Input value of [number={number}] must be a positive integer'
  raise ValueError(lowercase__ )
 lowerCAmelCase													=   [number]
 while number != 1:
  if number % 2 == 0:
   lowerCAmelCase													=   math.floor(math.sqrt(lowercase__ ) )
  else:
   lowerCAmelCase													=   math.floor(
       math.sqrt(lowercase__ ) * math.sqrt(lowercase__ ) * math.sqrt(lowercase__ ) )
  sequence.append(lowercase__ )
 return sequence


if __name__ == "__main__":
       import doctest

       doctest.testmod()












"""simple docstring"""
import math

def 		_SCREAMING_SNAKE_CASE (_UpperCAmelCase				:						int ):

 if 1 < number < 4:
  # 2 and 3 are primes
  return True
 elif number < 2 or number % 2 == 0 or number % 3 == 0:
  # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
  return False

 # All primes number are in format of 6k +/- 1
 for i in range(5     ,    int(math.sqrt(_UpperCAmelCase ) + 1 )     ,    6 ):
  if number % i == 0 or number % (i + 2) == 0:
   return False
 return True

def 		_SCREAMING_SNAKE_CASE (_UpperCAmelCase				:						int = 200_0000 ):
 return sum(num for num in range(3     ,    _UpperCAmelCase     ,    2 ) if is_prime(_UpperCAmelCase ) ) + 2 if n > 2 else 0


if __name__ == "__main__":
       print(f'''{solution() = }''')





