# [Haskell], <s>61</s> <s>60</s> <s>50</s> <s>48</s> 46 bytes

-2 bytes thanks to [xnor](https://codegolf.stackexchange.com/users/20260/xnor)

<!-- language-all: lang-hs -->

 f n=maximum[a|k<-[2..n],a<-[1..n],n`mod`k^a<1]

[Try it online!][TIO-j91nfn78]

[Haskell]: https://www.haskell.org/
[TIO-j91nfn78]: https://tio.run/##HcZNCsIwEAbQq2Sp8BkyMVUL7RE8QYh2QIshnbH4Ay68eywuHrwbP8t1mmodjfbCnyxvifwt3SZ6azWBl9F/Osj9MpQTd5SqcFbTG@H5eDar@ZH1Zce1iR5bBDTYYY8DWpADEciDQoB3Ds2CnA@p/gA "Haskell – Try It Online"

###45 bytes with an import:

 import NumberTheory
 maximum.map snd.factorize

[Try it Online!](https://tio.run/##DcmxDoIwFAXQ3a/oqMlN0z5aqQOfoJObMaZqCQ08IKUk6s9XhjOdzi99GIZSIs9TyuKy8jOkaxem9N21DftP5JUl@1ks41u2/pWnFH@hsI@jaMQW54fYzymOWbYHcSNUMLA4oobDCVpBa2iCNgakFOxGKzKoyNauIuPcvfwB)