def sum_primes(n):
"""Retrun the sum of the prime numbers less than n."""
total = 0
for x in sieveOfEra():
if x < n:
total += x
else:
return total
def smallest_dividable(n):
"""
Find the smallest number which is dividable by all numbers from 1 to n
utilizing prim factorization
"""
primes = []
smallest = 1
# Add all of the primes to the list primes, which are less than n.
for num in sieveOfEra():
if num <= n:
primes.append(num)
else:
break
# a calculates the highest power each prime can be raised to and still
# be less than n. Then we raise it to that power and multiply it by the
# smallest number place holder for each prime on the list.
for prime in primes:
a = floor(log(n) / log(prime))
smallest *= int(prime ** a)
return smallest
