Editing Semiperfect number (section)

== Properties ==
* Every [[multiple (mathematics)|multiple]] of a semiperfect number is semiperfect.{{sfnp|Zachariou|Zachariou|1972}}  A semiperfect number that is not [[divisible]] by any smaller semiperfect number is called ''primitive''.
* Every number of the form 2<sup>''m''</sup>''p'' for a natural number ''m'' and an [[parity (mathematics)|odd]] [[prime number]] ''p'' such that ''p'' < 2<sup>''m''+1</sup> is also semiperfect. 
** In particular, every number of the form 2<sup>''m''</sup>(2<sup>''m''+1</sup>&nbsp;−&nbsp;1) is semiperfect, and indeed perfect if 2<sup>''m''+1</sup>&nbsp;−&nbsp;1 is a [[Mersenne prime]].
* The smallest odd semiperfect number is [[945 (number)|945]].{{sfnp|Friedman|1993}}
* A semiperfect number is necessarily either perfect or [[abundant number|abundant]]. An abundant number that is not semiperfect is called a [[weird number]]. 
* With the exception of 2, all [[primary pseudoperfect number]]s are semiperfect. 
* Every [[practical number]] that is not a [[power of two]] is semiperfect.
* The [[natural density]] of the [[set (mathematics)|set]] of semiperfect numbers exists.{{sfnp|Guy|2004|p=75}}