Definition:Deficient Number/Definition 2

Definition

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

Let $\map {\sigma_1} n$ be the divisor sum function of $n$.

$n$ is deficient if and only if:

$\dfrac {\map {\sigma_1} n} n < 2$

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 known as

A deficient number is also known as a defective number.

Also see

• Equivalence of Definitions of Deficient Number

• Results about deficient numbers can be found here.