Algorithm to check if a number if a perfect number

Question

I am looking for an algorithm to find if a given number is a perfect number.

The most simple that comes to my mind is :

1. Find all the factors of the nu

Answer 1

If the input is even, see if it is of the form 2^(p-1)*(2^p-1), with p and 2^p-1 prime.

If the input is odd, return "false". :-)

See the Wikipedia page for details.

(Actually, since there are only 47 perfect numbers with fewer than 25 million digits, you might start with a simple table of those. Ask the interviewer if you can assume you are using 64-bit numbers, for instance...)