def count_divisors(n, primeList):
"""Get prime factorization, and count all possible combination of those
prime factors"""
countDict = count_occurances(gen_factorization(n, primeList))
# just the counts of the prime factors, not the facors themselves
# we dont care about them anymore
countList = countDict.values()
return reduce(operator.mul, (d+1 for d in countList) , 1)
def main(number):
nums_to_consider = range(2, number+1)
# How many times a prime is used to compose a given number in the list
primeUsage = {}
for num in nums_to_consider:
primeUsage[num] = 0
countDict = count_occurances(gen_factorization(num))
for dPrime in countDict.iterkeys():
primeUsage[dPrime] = max(countDict[dPrime], primeUsage[dPrime])
result = 1
for key in primeUsage:
if primeUsage[key]:
result *= (key ** primeUsage[key])
return result
def main (limit):
for n in gen_factorization(limit):
largestFactor = n
return largestFactor