def divisible_by(n):
output = {}
for i in xrange(1, n + 1):
factorized = mathtools.prime_factorization(i)
for number in factorized:
if number not in output:
output[number] = factorized[number]
if number in output and factorized[number] > output[number]:
output[number] = factorized[number]
return mathtools.factorized_to_number(output)
def largest_prime_factor(n):
factorization = mathtools.prime_factorization(n)
return max(factorization.keys())
