I’m Perfect!

Happy Birthday to Mr. Chase, today!

Today, I think I can safely say, is the last time my age will be a perfect number. The last time my age was perfect was when I was 6 years old. For those that forget the definition of a perfect number:

A number is perfect if it is the sum of its proper divisors (that is, the sum of its divisors, excluding itself).

For example, 6 is perfect because 1+2+3=6.

I’m not 6. How old *am* I?

So, how old am I?

If you’re a consummate mathematician, you have the first couple perfect numbers memorized, and this is an easy question. If you’ve never thought about perfect numbers, or you forget what the next one is, I challenge you to figure it out for yourself. I challenged my students today to figure out my age, and two of them got it out without my help.

For a real challenge, prove that there are infinitely many perfect numbers. (open problem!)

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