Definition:Quadruply Perfect Number

Definition

A quadruply perfect number is a positive integer $n$ such that the sum of its divisors is equal to $4$ times $n$.

Sequence of Quadruply Perfect Numbers

The sequence of quadruply perfect numbers begins:

$30 \, 240, 32 \, 760, 2 \, 178 \, 540, 23 \, 569 \, 920, 45 \, 532 \, 800, 142 \, 990 \, 848, 1 \, 379 \, 454 \, 720, \ldots$

Examples

$30 \, 240$ is Quadruply Perfect

$30 \, 240$ is quadruply perfect:

$\map {\sigma_1} {30 \, 240} = 120 \, 960 = 4 \times 30 \, 240$

Also known as

Some sources use the term fourfold perfect or four-fold perfect.

Also see

• Definition:Perfect Number
• Definition:Multiply Perfect Number
• Results about quadruply perfect numbers can be found here.