code: 
  
  
  '''simple docstring'''
  
  
  
  
  import math
  
  
  
  
  
  def 							a_       (						lowercase    )			->list:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				if n <= 0:
  								raise ValueError("Only positive integers have prime factors"    )
  				__lowerCamelCase		:      List[str]											=					[]
  				while n % 2 == 0:
  								pf.append(2    )
  								__lowerCamelCase		:      str											=					int(n / 2    )
  				for i in range(3							,						int(math.sqrt(lowercase    )    ) + 1							,						2    ):
  								while n % i == 0:
  												pf.append(lowercase    )
  												__lowerCamelCase		:      Dict											=					int(n / i    )
  				if n > 2:
  								pf.append(lowercase    )
  				return pf
  
  
  
  
  
  def 							a_       (						lowercase    )			->int:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				if n <= 0:
  								raise ValueError("Only positive numbers are accepted"    )
  				__lowerCamelCase		:      List[Any]											=					1
  				__lowerCamelCase		:      Dict											=					1
  				while n % 2 == 0:
  								temp += 1
  								__lowerCamelCase		:      str											=					int(n / 2    )
  				div *= temp
  				for i in range(3							,						int(math.sqrt(lowercase    )    ) + 1							,						2    ):
  								__lowerCamelCase		:      List[Any]											=					1
  								while n % i == 0:
  												temp += 1
  												__lowerCamelCase		:      Tuple											=					int(n / i    )
  								div *= temp
  				if n > 1:
  								div *= 2
  				return div
  
  
  
  
  
  def 							a_       (						lowercase    )			->int:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				if n <= 0:
  								raise ValueError("Only positive numbers are accepted"    )
  				__lowerCamelCase		:      List[Any]											=					1
  				__lowerCamelCase		:      Dict											=					1
  				while n % 2 == 0:
  								temp += 1
  								__lowerCamelCase		:      List[str]											=					int(n / 2    )
  				if temp > 1:
  								s *= (2**temp - 1) / (2 - 1)
  				for i in range(3							,						int(math.sqrt(lowercase    )    ) + 1							,						2    ):
  								__lowerCamelCase		:      Optional[int]											=					1
  								while n % i == 0:
  												temp += 1
  												__lowerCamelCase		:      List[Any]											=					int(n / i    )
  								if temp > 1:
  												s *= (i**temp - 1) / (i - 1)
  				return int(lowercase    )
  
  
  
  
  
  def 							a_       (						lowercase    )			->int:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				__lowerCamelCase		:      Optional[Any]											=					n
  				for x in set(prime_factors(lowercase    )    ):
  								s *= (x - 1) / x
  				return int(lowercase    )
  
  
  if __name__ == "__main__":
  				import doctest
  
  				doctest.testmod()
  
  
  
  
  
  
style_context: 
  
  
  '''simple docstring'''
  
  
  
  
  def 							a_       (						lowercase    )			->str:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				return " ".join(sorted(set(sentence.split()    )    )    )
  
  
  if __name__ == "__main__":
  				import doctest
  
  				doctest.testmod()
  
  
  
  
  
  