Definition:Radical of an Integer
From ProofWiki
Definition
The radical of an integer $n \in \Z$ is the product of the individual prime factors of $n$.
The radicals of the first few integers are given here:
| $n$ | Decomposition | $\operatorname{rad} \left({n}\right)$ | ||
|---|---|---|---|---|
| $1$ | $1$ | $1$ | ||
| $2$ | $2$ | $2$ | ||
| $3$ | $3$ | $3$ | ||
| $4$ | $2^2$ | $2$ | ||
| $5$ | $5$ | $5$ | ||
| $6$ | $2 \times 3$ | $6$ | ||
| $7$ | $7$ | $7$ | ||
| $8$ | $2^3$ | $2$ | ||
| $9$ | $3^2$ | $3$ | ||
| $10$ | $2 \times 5$ | $10$ | ||
| $11$ | $11$ | $11$ | ||
| $12$ | $2^2 \times 3$ | $6$ | ||
| $13$ | $13$ | $13$ | ||
| $14$ | $2 \times 7$ | $14$ | ||
| $15$ | $3 \times 5$ | $15$ | ||
| $16$ | $2^4$ | $2$ |
This sequence is A007947 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
The radical of $n$ can alternatively be described as the largest square-free integer which divides $n$.
