def primalHappiness(n): # find happy primes up to n, return list of them
fillHappiness(n)
primenumbers=primes(n)
happyPrimes=[]
for i in happiness:
if i in primenumbers:
happyPrimes.append(i)
return happyPrimes
def primeFactors(n):
"""a list of prime factors of n"""
result = []
upper_bound = 1 +int(n**0.5) # only have to seek to the square root
searchList = primes(upper_bound)
for divisor in searchList:
if divides(divisor, n):
result.append(divisor)
result += primeFactors(int(n // divisor))
break
# no factors found, so assume prime.
if result == []:
result.append(n)
return result
