Problem 30
Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:
1634 = 1 4 + 6 4 + 3 4 + 4 4
8208 = 8 4 + 2 4 + 0 4 + 8 4
9474 = 9 4 + 4 4 + 7 4 + 4 4
As 1 = 14 is not a sum it is not included.
The sum of these numbers is 1634 + 8208 + 9474 = 19316.
Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.
# 寻找一些数，他们各位数的5次方相加等于自身，求这些数的和。
i = 2
sum1 = 0
while i < 360000:
string = str(i)
l = [(int(x))**5 for x in string]
if i == sum(l):
print(i)
sum1 += i
i += 1
print(sum1)
思路：如果这个数为7位数，它一定小于7*9！=413343，所以这样的数不会是7位数或更大
如果这个数为6位数，它一定小于6*9！=354294，所以搜索上界就是它
结果：443839