Abundant number

Definition

A positive integer $n$ is abundant if the sum of its positive divisors other than $n$ is greater than $n$ . Equivalently, $\sigma(n) > 2n$ , where $\sigma$ is the sum of divisors.

Remarks

The smallest abundant number is $12$ , since $1 + 2 + 3 + 4 + 6 = 16 > 12$ . The smallest odd abundant number is $945$ . Each multiple $kn$ with $k \ge 2$ of a perfect number $n$ is abundant.

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

Tag	`0VS0MP1P5H`
URI	`m2://0VS0MP1P5H`
Kind	definition
Writing	W1 stated
MSC	11A25
Defines	Abundant number
Uses	Sum of divisors

Abundant number

Definition

Remarks

Reading path

Further reading

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