### Dudeney Number

A Dudeney number is a positive integer that is a perfect cube such that the sum of its decimal digits is the cube root of the number. The name derives from Henry Dudeney, who noted the existence of these numbers in one of his puzzles.

There are exactly six Dudeney numbers.

1 = 1 x 1 x 1 ; 1 = 1

512 = 8 x 8 x 8 ; 8 = 5 + 1 + 2

4913 = 17 x 17 x 17 ; 17 = 4 + 9 + 1 + 3

5832 = 18 x 18 x 18 ; 18 = 5 + 8 + 3 + 2

17576 = 26 x 26 x 26 ; 26 = 1 + 7 + 5 + 7 + 6

19683 = 27 x 27 x 27 ; 27 = 1 + 9 + 6 + 8 + 3

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