Deficient number

Definition

A positive integer $n$ is deficient if the sum of its positive divisors other than $n$ is less than $n$. Equivalently, $\sigma(n) < 2n$, where $\sigma$ is the sum of divisors.

Remarks

Each prime $p$ is deficient, since its only smaller divisor is $1$. More generally, each prime power is deficient. For example, $1 + 2 + 4 = 7 < 8$. Each divisor of a deficient number or of a perfect number, other than the number itself, is deficient.

Explanations

L1 human

A deficient number has "too few" divisors: its smaller divisors add up to less than the number. Most small numbers are deficient, for example $1, 2, 3, 4, 5, 7, 8, 9, 10$.