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# Dudeney number

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 Title: Dudeney number Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### 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, #120.