Semiperfect Numbers Day - December 18

Happy Semiperfect Numbers Day! 

While perfect numbers are numbers that are equal to the sum of all their proper divisors, semiperfect numbers are equal to the sum of some of their proper divisors. (Yes, this means that all perfect numbers are also semiperfect numbers.)

Similar to perfect numbers, semiperfect numbers don't seem to have a lot of application but are more of numerical oddities. Here are the smallest semiperfect numbers, including a couple that are also perfect numbers:

And here's the arithmetic that shows why the smaller numbers are or are not semiperfect numbers.

We celebrate Semiperfect Numbers Day on December 18 because 12/18 is the latest (American style) date that can be formed using consecutive semiperfect numbers.



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