def get_divisors(number):
ps = prime_factors(number)
divisors = set(ps)
divisors.add(1)
l = 2
while l <= len(ps):
for c in itertools.combinations(ps, l):
divisors.add(reduce(lambda x, y: x * y, c))
l += 1
return divisors
def smallest_multiple(min_val, max_val):
min_val = max(min_val, 2)
factor_counts = dict()
for i in range(min_val, max_val+1):
i_factors = prime_factors(i)
for factor in i_factors:
i_factor_count = i_factors.count(factor)
if factor in factor_counts:
factor_count = max(factor_counts[factor], i_factor_count)
else:
factor_count = i_factor_count
factor_counts[factor] = factor_count
product = 1
for factor, count in factor_counts.iteritems():
product = product * (factor ** count)
return product
def count_divisors(number):
num_ps = len(prime_factors(number))
num_divisors = 1
for k in range(1, num_ps+1):
num_divisors += num_combinations(num_ps, k)
return num_divisors
