Dudeney number

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 seven such integers (sequence A061209 in the OEIS):

0	= 0 x 0 x 0	; 0   = 0
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.

External links

• Generalized Dudeney Numbers
• Proving There are Only Six Dudeney Numbers