






'''simple docstring'''







def 			__UpperCamelCase				(			lowercase_					:     int      ):
       """simple docstring"""




       a_	    = [True for i in range(n + 1      )]
       a_	    = [i - 1 for i in range(n + 1      )]
       a_	    = []
       for i in range(2      ,					n + 1      ):
              if is_prime[i]:
                     primes.append(lowercase_      )
              for j in range(0      ,					len(lowercase_      )      ):
                     if i * primes[j] >= n:
                            break
                     a_	    = False

                     if i % primes[j] == 0:
                            a_	    = totients[i] * primes[j]
                            break

                     a_	    = totients[i] * (primes[j] - 1)

       return totients


if __name__ == "__main__":
  import doctest

  doctest.testmod()












'''simple docstring'''







def 			__UpperCamelCase				(			lowercase_					:     int      ):
       """simple docstring"""




       if not isinstance(lowercase_      ,					lowercase_      ):
              raise ValueError('double_factorial() only accepts integral values'      )
       if num < 0:
              raise ValueError('double_factorial() not defined for negative values'      )
       a_	    = 1
       for i in range(lowercase_      ,					0      ,					-2      ):
              value *= i
       return value


if __name__ == "__main__":
  import doctest

  doctest.testmod()




