Definition:Deficient 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 deficient if and only if $A \left({n}\right) < 0$.


Definition 2

Let $\sigma \left({n}\right)$ be the sigma function of $n$.

$n$ is deficient if and only if:

$\dfrac {\sigma \left({n}\right)} n < 2$


Definition 3

$n$ is deficient if and only if it is greater than its aliquot sum.


Sequence

The sequence of deficient numbers begins:

$2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, \ldots$


Also see

  • Results about deficient numbers can be found here.


Sources