Dudeney number
From Infogalactic: the planetary knowledge core
A Dudeney number is a positive integer that is a perfect cube such that the sum of its decimal digits is equal to the cube root of the number. There are exactly six such integers (sequence A061209 in OEIS):
| 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 |
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.
References
- H. E. Dudeney, 536 Puzzles & Curious Problems, Souvenir Press, London, 1968, p 36, #120.
