Generating random permutations is quite a different problem from creating random numbers. The standard algo for random permutations is the Fisher-Yates Shuffle.

https://en.wikipedia.org/wiki/Fisher–Yates_shuffle

ETA: As you don't want to store the permutation, you might want to pick a number randomly from 1 to n!, and then generate the permutation on the fly up to the desired element, using the techniques outlined here:

https://stackoverflow.com/questions/29236556/how-can-i-calcu...