October 2011 Fiendish Function

The Fiendish Function posed during October 2011 had the following sample guesses and replies:

• GUESS
• REPLY
• 1
• 1
• 2
• 4
• 3
• 9
• 4
• 7
• 5
• 7
• 10
• 1

The rule was: "Square the number, then add the digits together".

Suppose the guess was 13:

• Square the number, giving 169.
• Find the number's divisors, giving 1, 6, 9
• Add these together, giving 16.

So the result is 16.