#R, 52 bytes

`if`((n=scan())<2,1,prod(unique(c(1,gmp::factorize(n))))

reads n from stdin. Requires the gmp library to be installed (so TIO won't work). Uses the same approach as many of the above answers, but it crashes on an input of 1, because factorize(1) returns an empty vector of class bigz, which crashes unique, alas.

R, 52 bytes

`if`((n=scan())<2,1,prod(unique(c(1,gmp::factorize(n))))

reads n from stdin. Requires the gmp library to be installed (so TIO won't work). Uses the same approach as many of the above answers, but it crashes on an input of 1, because factorize(1) returns an empty vector of class bigz, which crashes unique, alas.

#R, 51 bytes

s=1:(n=scan());f=s[!s%in%s^2];max(max(f[n%%f<1]),1)

reads n from stdin. requires two max calls since the way I've done it, an input of 1 returns -Inf for the first max. f is the first n integers that aren't squares.

Try it online

#R, 52 bytes

`if`((n=scan())<2,1,prod(unique(c(1,gmp::factorize(n))))

reads n from stdin. Requires the gmp library to be installed (so TIO won't work). Uses the same approach as many of the above answers, but it crashes on an input of 1, because factorize(1) returns an empty vector of class bigz, which crashes unique, alas.