


def     UpperCamelCase    (      _a = 1_0_0_0_0_0_0		)					->							int:
     '''simple docstring'''





     lowercase_       :Tuple     =       set(range(3       ,		_a       ,		2		)		)
     primes.add(2		)
     for p in range(3       ,		_a       ,		2		):
          if p not in primes:
               continue
          primes.difference_update(set(range(p * p       ,		_a       ,		_a		)		)		)

     lowercase_       :List[str]     =       [float(_a		) for n in range(limit + 1		)]

     for p in primes:
          for n in range(_a       ,		limit + 1       ,		_a		):
               phi[n] *= 1 - 1 / p

     return int(sum(phi[2:]		)		)


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





def     UpperCamelCase    (      _a		)					->							int:
     '''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:
          lowercase_       :str     =       f"The input value of [n={number}] has to be > 0"
          raise ValueError(_a		)
     else:
          lowercase_       :List[str]     =       sylvester(number - 1		)
          lowercase_       :Union[str, Any]     =       num - 1
          lowercase_       :List[str]     =       num
          return lower * upper + 1


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

