



"""simple docstring"""
def 			_SCREAMING_SNAKE_CASE						(__lowerCAmelCase = 1_00_00_00							) ->						int:







  '''simple docstring'''


  lowercase_								= [i - 1 for i in range(limit + 1							)]

  for i in range(2 ,  limit + 1							):
    if phi[i] == i - 1:
      for j in range(2 * i ,  limit + 1 ,  __lowerCAmelCase							):
        phi[j] -= phi[j] // i

  return sum(phi[2 : limit + 1]							)


if __name__ == "__main__":
       print(solution())






"""simple docstring"""
def 			_SCREAMING_SNAKE_CASE						(__lowerCAmelCase=2_81_23							) ->						Optional[Any]:







  '''simple docstring'''


  lowercase_								= [1] * (limit + 1)

  for i in range(2 ,  int(limit**0.5							) + 1							):
    sum_divs[i * i] += i
    for k in range(i + 1 ,  limit // i + 1							):
      sum_divs[k * i] += k + i

  lowercase_								= set()
  lowercase_								= 0

  for n in range(1 ,  limit + 1							):
    if sum_divs[n] > n:
      abundants.add(__lowerCAmelCase							)

    if not any((n - a in abundants) for a in abundants							):
      res += n

  return res


if __name__ == "__main__":
       print(solution())

