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A perfect number is a number that is the sum of its proper divisors: $$28 = 1 + 2 + 4 + 7 + 14$$

Is there a name for numbers whose only proper divisors are $1$, $2$, and $N/2$? For example

$6$ is divisible by $1$, $2$, and $3$

$8$ is divisible by $1$, $2$, and $4$

$34$ is divisible by $1$, $2$, and $17$

Is there a name for these numbers?

  • 7
    Yes, I would call them even numbers.2010-10-14
  • 0
    Perhaps Wayne meant 34 is divisible by 17? And perhaps he also meant those are its _only_ divisors.2010-10-14
  • 0
    @Joseph: Yes, that is why I only left a comment, instead of posting an answer. btw, the typo of 24->34 seems to be more likely than the typo of 17->12 though :-) I guess it depends on the keyboard layout :-)2010-10-14
  • 0
    @Moron: Your "even number" comment made me laugh! :-)2010-10-14
  • 1
    I guess you would call them even semiprimes, or 8. http://en.wikipedia.org/wiki/Semiprime2010-10-14
  • 0
    @Moron: Funny, but for now I've rendered your first comment senseless. I also went the 12->17 route, believing that Joseph's interpretation is correct. @Wayne: If my attempt at correcting your question is incorrect or otherwise not to your liking, you can undo the changes.2010-10-14
  • 14
    Also known as "twice a prime, or 8".2010-10-14
  • 3
    I suppose 8 is twice a prime in the sense of Grothendieck (the same sense in which 57 is prime).2010-10-14
  • 1
    Something "unpleasant" that the comment of Aryabhata has received seven votes as "useful".2018-07-29

1 Answers 1

7

Aside from 8 and arguably 2, these are the even semiprimes, Sloane's A100484.