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.

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Arithmetic function definition
Divisibility definition
Divisors of a natural number definition
Divisor function definition
Sum of divisors definition
Deficient number definition

Tag	`0G01TS1RRP`
URI	`m2://0G01TS1RRP`
Kind	definition
Writing	W1 stated
MSC	11A25
Defines	Deficient number
Uses	Sum of divisors

Deficient number

Definition

Remarks

Reading path

Further reading

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