Dudeney number

A Dudeney number is an integer that is a Perfect cube such that the sum of its digits forms the cube root of the number. The name derives from Henry Dudeney, who noted the existence of these numbers in one of his puzzles, Root Extraction, where a professor in retirement at Colney Hatch postulates this as a general method for root extraction.

They are very few in number:

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

H. E. Dudeney, 536 Puzzles & Curious Problems, Souvenir Press, London, 1968, p 36

Links

* A061209 in OEIS