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 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.
各位数字的五次幂
令人惊讶的是，只有三个数可以写成其各位数字的四次幂之和：
\[1634 = 1^4 + 6^4 + 3^4 + 4^4 \\ 8208 = 8^4 + 2^4 + 0^4 + 8^4 \\ 9474 = 9^4 + 4^4 + 7^4 + 4^4\]
由于 14 并不是求和，所以这里不计入内。
上面这三个数的和是 1634 + 8208 + 9474 = 19316。
找出所有可以写成其各位数字的五次幂之和的数，并求这些数的和。
考虑到 9^5 * 5 = 295245 而 9^5 * 6 = 354294，满足条件的数字最多只可能是六位数了：
(let ((ls '()))
(cl-loop for i from 2 to 999999
do (let ((numls (mapcar (lambda (x) (- x ?0))
(string-to-list (number-to-string i)))))
(when (= (cl-reduce (lambda (s a) (+ s (expt a 5)))
numls
:initial-value 0)
i)
(push i ls))))
ls)
=> (194979 93084 92727 54748 4151 4150)
(+ 194979 93084 92727 54748 4151 4150)
=> 443839