'''simple docstring'''




def _lowercase	(      lowerCamelCase__						)					->       Union[str, Any]:





       """simple docstring"""


       assert isinstance(__A							,    __A						), f"""The input value of [n={number}] is not an integer"""

       if number == 1:
              return 2
       elif number < 1:
              __UpperCAmelCase  :				Optional[int]       				=		f"""The input value of [n={number}] has to be > 0"""
              raise ValueError(__A						)
       else:
              __UpperCAmelCase  :				Optional[Any]       				=		sylvester(number - 1						)
              __UpperCAmelCase  :				Tuple       				=		num - 1
              __UpperCAmelCase  :				Optional[Any]       				=		num
              return lower * upper + 1


if __name__ == "__main__":
   print(f"""The 8th number in Sylvester's sequence: {sylvester(8)}""")







'''simple docstring'''




from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors

def _lowercase	(      lowerCamelCase__						)					->       int:





       """simple docstring"""


       __UpperCAmelCase  :				Any       				=		prime_factors(lowerCamelCase__						)
       if is_square_free(lowerCamelCase__						):
              return -1 if len(lowerCamelCase__						) % 2 else 1
       return 0


if __name__ == "__main__":
   import doctest

   doctest.testmod()






