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.

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Of the form
a × 2^b ± 1

Other polynomial
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2-dimensional

centered	Centered triangular Centered square Centered pentagonal Centered hexagonal Centered heptagonal Centered octagonal Centered nonagonal Centered decagonal Star

non-centered	Triangular Square Square triangular Pentagonal Hexagonal Heptagonal Octagonal Nonagonal Decagonal Dodecagonal

3-dimensional

centered	Centered tetrahedral Centered cube Centered octahedral Centered dodecahedral Centered icosahedral

non-centered	Tetrahedral Octahedral Dodecahedral Icosahedral Stella octangula

pyramidal	Square pyramidal Pentagonal pyramidal Hexagonal pyramidal Heptagonal pyramidal

4-dimensional

centered	Centered pentachoric Squared triangular

non-centered	Pentatope

Pseudoprimes

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By properties of σ(n)	Abundant Almost perfect Arithmetic Colossally abundant Descartes Hemiperfect Highly abundant Highly composite Hyperperfect Multiply perfect Perfect Practical number Primitive abundant Quasiperfect Refactorable Sublime Superabundant Superior highly composite Superperfect

By properties of Ω(n)	Almost prime Semiprime

By properties of φ(n)	Highly cototient Highly totient Noncototient Nontotient Perfect totient Sparsely totient

By properties of s(n)	Amicable Betrothed Deficient Semiperfect

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