


def 						_lowerCAmelCase							(     _lowerCAmelCase = 100_0000			)    ->						int:


						'''simple docstring'''






						__snake_case				=		[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())









from __future__ import annotations





def 						_lowerCAmelCase							(     _lowerCAmelCase			)    ->						list[int]:


						'''simple docstring'''






						__snake_case				=		2
						__snake_case				=		[]
						while i * i <= n:
												if n % i:
																		i += 1
												else:
																		n //= i
																		factors.append(_lowerCAmelCase			)
						if n > 1:
												factors.append(_lowerCAmelCase			)
						return factors


if __name__ == "__main__":
	import doctest

	doctest.testmod()





