Are all Almost Perfect Numbers Even?

Open Question

It is known by Power of 2 is Almost Perfect that all powers of $2$ are almost perfect.

But it is not known whether there exist any odd almost perfect numbers. None have ever been found.


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $16$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $16$
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