Definition:Radical of Integer

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Definition

Let $n \in \Z$ be an integer.

Definition 1

The radical of $n$ is the product of the individual prime factors of $n$.


Definition 2

The radical of $n$ is the largest square-free integer which divides $n$.


Sequence

The sequence of radicals of the integers beings:

Radical of Integer
$n$ Decomposition $\map \Rad n$
$1$ $1$ $1$
$2$ $2$ $2$
$3$ $3$ $3$
$4$ $2^2$ $2$
$5$ $5$ $5$
$6$ $2 \times 3$ $6$
$7$ $7$ $7$
$8$ $2^3$ $2$
$9$ $3^2$ $3$
$10$ $2 \times 5$ $10$
$11$ $11$ $11$
$12$ $2^2 \times 3$ $6$
$13$ $13$ $13$
$14$ $2 \times 7$ $14$
$15$ $3 \times 5$ $15$
$16$ $2^4$ $2$


Also known as

The radical of an integer $n$ is also known as the square-free kernel of $n$.


Also see

  • Results about radicals of integers can be found here.


Sources