Yes I think it should be less than or equal to, equal in the case of n=1.
If you allow n to be a real number you can get it to be less than 1 but the maximum is
![](https://latex.codecogs.com/png.latex?\bg_white \sqrt[e]{e})
so for positive integers the maximum is
![](https://latex.codecogs.com/png.latex?\bg_white \sqrt[3]{3}\approx1.44)
and minimum is 1. So a tighter bound for positive integers is
You can see it more clearly in the graph of
Range for real
![](https://latex.codecogs.com/png.latex?\bg_white x>0)
is
Range for positive integers
![](https://latex.codecogs.com/png.latex?\bg_white n)
is
![Screen Shot 2023-03-21 at 8.41.05 pm.png](/data/attachments/38/38029-4f6acf7b279df9890ea36d89144f2178.jpg)