Definition:Quasiperfect Number

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Definition

Let $n \in \Z_{\ge 0}$ be a positive integer.


Definition 1

Let $A \left({n}\right)$ denote the abundance of $n$.

$n$ is quasiperfect if and only if $A \left({n}\right) = 1$.


Definition 2

$n$ is quasiperfect if and only if:

$\sigma \left({n}\right) = 2 n + 1$

where $\sigma \left({n}\right)$ denotes the $\sigma$ function of $n$.


Definition 3

$n$ is quasiperfect if and only if it is exactly one less than the sum of its aliquot parts.


Also known as

Some sources use the terms:

  • Quasi-perfect
  • Slightly excessive


Also see

  • Results about quasiperfect numbers can be found here.