def problem73a():
	total = 0
	from factorGenerating import genFactors
	for d in genFactors(12000):
		if d in [(1,)]: continue
		for n in genFactors(product(d)):
			r = product(n)/product(d)
			if relPrimeFromFactors(n,d) == 1 and r > 1/3 and r < 1/2:
				total += 1
	return total
def problem231():
	n = 20000000
	c = 15000000
	total = 1
	for factor in genFactors(n):
		prod = product(factor)		
		if n - c < prod <= n:
			total += sum(factor)
		if 1<= prod <= c:
			total -= sum(factor)
	return total