Find the sum of all the numbers that can be written as the sum of fifth powers of their digits. Run this solution at repl.io here.
sum_fifth_powers = []
#low limit = 10, otherwise it is not a sum of digits
# upper limit = 6 * 9^5 (6 digits all with base 9): just a nice guess
for num in range(10,6*(9**5)):
if num == sum([int(digit)**5 for digit in str(num)]):
sum_fifth_powers.append(num)
print(sum(sum_fifth_powers))