(June 9, 2020 at 1:49 am)FlatAssembler Wrote:polymath257 Wrote:The corresponding distribution function is -ln(t).I am not sure what you mean. Distribution function has to be bound by 0 and 1, right? While -ln(1)=0, -ln(0)=infinity.
Besides, -ln(t) would be a homogenous function, always falling. The distribution of numbers in the multiplication table has short intervals of growth (that my web-app draws red).
I went for the derivative, which is the density function. The distribution function you are thinking of will be t(1-ln(t)). At t=0, the logarithm goes to -infty, but at a rate which makes the product go to 0.
The growth that you see in the tables is because of the granularity (large percentage jump between the numbers you use). In the limit, that goes away.
