# Definition:Powerful Number

## Theorem

A powerful number is a positive integer such that each of its prime factors appears with multiplicity at least $2$.

That is, each of its prime factors occurs at least squared.

### Sequence

The sequence of powerful numbers begins:

$1, 4, 8, 9, 16, 25, 27, 32, 36, 49, \ldots$

## Also known as

A powerful number can also be referred to as a squareful, square full, square-full or 2-full number.

## Also see

• Results about powerful numbers can be found here.