In the previous post, we looked at numbers that are amicable. Along a similar line of thinking, let’s look at perfect numbers. A small example of a perfect number is 6. What makes it perfect? Once again, I am going to ask you to take a minute and find the proper positive divisors of 6. Go on! I’ll give you time. (Don’t peek until you are done!)
6: 1, 2, 3
Now, like we did previously, find the sum of these proper divisors.
1 + 2 + 3 = 6
The proper divisors of 6 add up to 6. Cool!
Any positive integer that has proper divisors adding up to itself is a perfect number. Can you think of others? The first 4 were found over 2,000 years ago. Current findings use a similar line of thinking to that for finding Mersenne primes. Turns out that perfect numbers and Mersenne primes are closely related. I will share more on that in the next post. Until then, happy hunting!