A Python program to check if a given number is a Dudeney number or not.

 

A Dudeney number is a positive integer that is a perfect cube, and the sum of its decimal digits is equal to the cube root of the number. The name "Dudeney" comes from Henry Dudeney, a famous English puzzlist who discovered these numbers.

In other words, a positive integer n is a Dudeney number if:

n = m^3, where m is also a positive integer

and

the sum of the decimal digits of n is equal to the cube root of n.

For example, 512 is a Dudeney number because:

512 = 8^3 5 + 1 + 2 = 8

The first few Dudeney numbers are:

1, 512, 4913, 5832, 17576, 19683, 35937, 46656, 64000, 68921, ...

Note that there are infinitely many Dudeney numbers, but they are relatively rare.

Here's a Python program to check if a given number is a Dudeney number or not:

python
number = int(input("Enter a number: "))

# Calculate the cube root of the number
cube_root = round(number**(1/3))

# Calculate the sum of the digits of the number
digit_sum = sum(int(d) for d in str(number))

# Check if the number is a Dudeney number
if number == cube_root**3 and digit_sum == cube_root:
    print(number, "is a Dudeney number")
else:
    print(number, "is not a Dudeney number")

In this program, I first take the input number from the user. I then calculate the cube root of the number using the **(1/3) operator and rounding it to the nearest integer using the round() function.

I then calculate the sum of the digits of the number using a generator expression and the sum() function.

Finally, I check if the number is a Dudeney number by comparing it to the cube of the cube root and the sum of the digits to the cube root. If both conditions are satisfied, I print a message saying that the number is a Dudeney number. Otherwise, I print a message saying that the number is not a Dudeney number.