def euler():
# dictionary containing the highest power of each prime factor
zipped_factors = {}
# for each number in the desired range
for number in range(2, HIGHEST_DIVISOR + 1):
# calculate its prime factors
factors = prime.multiset_prime_factors(number)
# for each of those factors, and its power
for factor, power in factors.items():
# if that factor's power is higher than the one we had before
if (not factor in zipped_factors
or zipped_factors [factor] < power):
# set the factor's power to this power
zipped_factors [factor] = power
# calculate the product of the prime factors elevated to the given powers
accumulator = 1
for factor, power in zipped_factors.items():
accumulator *= factor ** power
# return that product
return accumulator
def prime_factor_count(n):
"""Returns the number of distinct prime factors of a number."""
return len(prime.multiset_prime_factors(n))