If we define a function (aka Gronwall’s function) as: $$F(n)=\frac{\sigma(n)}{n \log \log n}$$
Then for $n>15$, it does have an upper bound. I want to know what's that specific upper bound is?
Also when exactly does the maxima of the divisor sum function ${\sigma(n)}$ occur? Is it at superabundant numbers or something else?
I know that the minima occurs at prime numbers where if n is a prime number then $\sigma(n)=n+1$, but I'm not sure about it's maxima.
This question was inspired from the answer given by Will Jagy here: https://math.stackexchange.com/q/3300005