This site is supported by donations to The OEIS Foundation.

# N divided by the largest squarefree divisor of n

${\displaystyle {\frac {n}{{\rm {rad}}(n)}}=n\prod _{{p\mid n} \atop {p~{\rm {prime}}}}{\frac {1}{p}},\,}$

where ${\displaystyle \scriptstyle {\rm {rad}}(n)\,}$ is the squarefree kernel of ${\displaystyle \scriptstyle n\,}$.

This is a multiplicative arithmetic function, e.g.

${\displaystyle {\frac {mn}{{\rm {rad}}(mn)}}={\frac {m}{{\rm {rad}}(m)}}\cdot {\frac {n}{{\rm {rad}}(n)}},\ (m,n)\,=\,1,\,}$

where ${\displaystyle \scriptstyle (m,\,n)\,}$ is the gcd function.

## Related formulae

The compositorial of ${\displaystyle \scriptstyle n\,}$ is given by:

${\displaystyle {\frac {n!}{n\#}}={\frac {n!}{{\rm {rad}}(n!)}}.\,}$

## Sequences

A003557 ${\displaystyle \scriptstyle n\,}$ divided by largest squarefree divisor of ${\displaystyle \scriptstyle n,\ n\,\geq \,1\,}$.

{1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 2, 1, 1, 1, 8, 1, 3, 1, 2, 1, 1, 1, 4, 5, 1, 9, 2, 1, 1, 1, 16, 1, 1, 1, 6, 1, 1, 1, 4, 1, 1, 1, 2, 3, 1, 1, 8, 7, 5, 1, 2, 1, 9, 1, 4, 1, 1, 1, 2, 1, 1, 3, 32, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 5, 2, ...}