Problem Statement

For the purposes of this task, an own digits power sum is a decimal integer which is N digits long and is equal to the sum of its individual digits raised to the power N.

The three digit integer 153 is an own digits power sum because 1³ + 5³ + 3³ = 1 + 125 + 27 = 153.

Find and show here all own digits power sums for N = 3 to N = 8 inclusive. Optionally, do the same for N = 9 which may take a while for interpreted languages.

Let's start with the solution: