




'''simple docstring'''



from __future__ import annotations
def 				SCREAMING_SNAKE_CASE_				(							__A       :				float | int ,  __A       :				float | int ,  __A       :				float | int ,  )				->				list[float | int]:
   if not all((nth_term, start_term_a, common_ratio_r)						):
      return []
   _SCREAMING_SNAKE_CASE =   []
   _SCREAMING_SNAKE_CASE =   1
   _SCREAMING_SNAKE_CASE =   common_ratio_r
   for _ in range(int(__A						)						):
      if not series:
         series.append(__A						)
      else:
         power += 1
         series.append(float(start_term_a * multiple						)						)
         _SCREAMING_SNAKE_CASE =   pow(float(__A						) ,  __A						)
   return series


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 lowerCamelCase_	 =		float(input('Enter the last number (n term) of the Geometric Series'))
 lowerCamelCase_	 =		float(input('Enter the starting term (a) of the Geometric Series'))
 lowerCamelCase_	 =		float(
     input('Enter the common ratio between two terms (r) of the Geometric Series')
 )
 print('Formula of Geometric Series => a + ar + ar^2 ... +ar^n')
 print(geometric_series(nth_term, start_term_a, common_ratio_r))







'''simple docstring'''



import math
def 				SCREAMING_SNAKE_CASE_				(							__A       :				Tuple						)				->				List[Any]:
   _SCREAMING_SNAKE_CASE =   0
   if n % 2 == 0:
      count += 1
      while n % 2 == 0:
         _SCREAMING_SNAKE_CASE =   int(n / 2						)
    # the n input value must be odd so that
    # we can skip one element (ie i += 2)

   _SCREAMING_SNAKE_CASE =   3

   while i <= int(math.sqrt(__A						)						):
      if n % i == 0:
         count += 1
         while n % i == 0:
            _SCREAMING_SNAKE_CASE =   int(n / i						)
      _SCREAMING_SNAKE_CASE =   i + 2

   # this condition checks the prime
   # number n is greater than 2

   if n > 2:
      count += 1
   return count


if __name__ == "__main__":
 lowerCamelCase_	 =		51_24_21_83
 print(f'''The number of distinct prime factors is/are {exact_prime_factor_count(n)}''')
 print(f'''The value of log(log(n)) is {math.log(math.log(n)):.4f}''')

