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The n divided by the largest squarefree divisor of n (n divided by the squarefree kernel of n) function is
![{\displaystyle {\frac {n}{{\rm {rad}}(n)}}=n\prod _{{p\mid n} \atop {p~{\rm {prime}}}}{\frac {1}{p}},\,}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/cfffce933bf59a0e308997147d826e91242925d1)
where
is the squarefree kernel of
.
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,\,}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/ff3de2c8af6b6b71c45116c6d19da4a97de3bd18)
where
is the gcd function.
Related formulae
The compositorial of
is given by:
![{\displaystyle {\frac {n!}{n\#}}={\frac {n!}{{\rm {rad}}(n!)}}.\,}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/ca399ad688413de70d6a4814f2ce62f2295e42ef)
Sequences
A003557
divided by largest squarefree divisor of
.
- {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, ...}
See also