def F(n, primelist = None, primefactorization = None):
		f = primes2.factors(n, primelist, primefactorization)
		s = 0 
		for x in f:
			s+= (mu(x)*fn((n/x), primelist))
		return s 
	def F(n, primelist = None, primefactorization = None):
		f = primes2.factors(n, primelist, primefactorization)
		s = 0
		for x in f:
			s += fn(x, primelist)
		return s