Definition:Quasiperfect Number

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:

$\map {\sigma_1} n = 2 n + 1$

where $\map {\sigma_1} n$ denotes the divisor sum 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

• Equivalence of Definitions of Quasiperfect Number

• Definition:Perfect Number
• Definition:Almost Perfect Number

• Definition:Deficient Number
• Definition:Abundant Number

• Definition:Abundance
• Definition:Abundancy Index

• Do Quasiperfect Numbers Exist?

• Results about quasiperfect numbers can be found here.