From Wikipedia: 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.
For example:
512=(5+1+2)^3
4913=(4+9+1+3)^3
19683=(1+9+6+8+3)^3
Write a function that returns true if a number is a Dudeney number and false otherwise.
Assume all numbers are of base 10.
If a number is negative, assume that only the leading digit carries the negative sign e.g. -4913 -> (-4+9+1+3)^3
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is there any negative dudeney number?
Depends upon how you define them.
If you are taking - sign outside the cube of the sum, every negative number corresponding to the positive Dudeney number is a Dudeney number.
If you define by the way OP has defined, -1 qualifies as a Dudeney number.