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 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.

External links

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