Dudeney number

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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 the 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.

External links

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