A few weeks ago I made up a "fake prime function" to illustrate that a certain property wasn't really a property specific to primes. I notice @johndcook wrote about it a couple of times
https://www.johndcook.com/blog/2023/08/21/fake-primes/
https://mathstodon.xyz/@johndcook/110927666845223894
In the back of my mind was Cramer's "model" of the primes although I was interested in different statistical properties https://terrytao.wordpress.com/tag/cramers-random-model/
@KodeGhinn @johndcook The density of the primes goes roughly like 1/log(n) and nlog(n) is good enough to get into the right ballpark to match the graph in the original question.