code: 
  
  
  
  """simple docstring"""
  
  
  
  
  import math
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		Optional[int]       )						->     Optional[Any]:
  
  
  
  
  
       '''simple docstring'''
  
       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(SCREAMING_SNAKE_CASE__       ) + 1       )		,						6       ):
            if number % i == 0 or number % (i + 2) == 0:
                 return False
       return True
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		Dict = 600_851_475_143       )						->     Any:
  
  
  
  
  
       '''simple docstring'''
  
       try:
            _UpperCAmelCase    :			List[str]              =					int(SCREAMING_SNAKE_CASE__       )
       except (TypeError, ValueError):
            raise TypeError("Parameter n must be int or castable to int."       )
       if n <= 0:
            raise ValueError("Parameter n must be greater than or equal to one."       )
       _UpperCAmelCase    :			str              =					0
       if is_prime(SCREAMING_SNAKE_CASE__       ):
            return n
       while n % 2 == 0:
            n //= 2
       if is_prime(SCREAMING_SNAKE_CASE__       ):
            return n
       for i in range(3		,						int(math.sqrt(SCREAMING_SNAKE_CASE__       )       ) + 1		,						2       ):
            if n % i == 0:
                 if is_prime(n // i       ):
                      _UpperCAmelCase    :			Union[str, Any]              =					n // i
                      break
                 elif is_prime(SCREAMING_SNAKE_CASE__       ):
                      _UpperCAmelCase    :			Dict              =					i
       return max_number
  
  
  if __name__ == "__main__":
   print(F"{solution() = }")
  
style_context: 
  
  
  
  """simple docstring"""
  
  
  
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		list       )						->     bool:
  
  
  
  
  
       '''simple docstring'''
  
       if not isinstance(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       ):
            raise ValueError("Input series is not valid, valid series - [1, 2/3, 2]"       )
       if len(SCREAMING_SNAKE_CASE__       ) == 0:
            raise ValueError("Input list must be a non empty list"       )
       if len(SCREAMING_SNAKE_CASE__       ) == 1 and series[0] != 0:
            return True
       _UpperCAmelCase    :			Tuple              =					[]
       _UpperCAmelCase    :			Any              =					len(SCREAMING_SNAKE_CASE__       )
       for i in range(0		,						SCREAMING_SNAKE_CASE__       ):
            if series[i] == 0:
                 raise ValueError("Input series cannot have 0 as an element"       )
            rec_series.append(1 / series[i]       )
       _UpperCAmelCase    :			Dict              =					rec_series[1] - rec_series[0]
       for index in range(2		,						SCREAMING_SNAKE_CASE__       ):
            if rec_series[index] - rec_series[index - 1] != common_diff:
                 return False
       return True
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		list       )						->     float:
  
  
  
  
  
       '''simple docstring'''
  
       if not isinstance(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       ):
            raise ValueError("Input series is not valid, valid series - [2, 4, 6]"       )
       if len(SCREAMING_SNAKE_CASE__       ) == 0:
            raise ValueError("Input list must be a non empty list"       )
       _UpperCAmelCase    :			Any              =					0
       for val in series:
            answer += 1 / val
       return len(SCREAMING_SNAKE_CASE__       ) / answer
  
  
  if __name__ == "__main__":
   import doctest
  
   doctest.testmod()
  