This is the sequence of prime numbers which are the elementary building blocks for the superior highly composite numbers:

$2, 3, 2, 5, 2, 3, 7, 2, 11, 13, 2, 3, 5, 17, 19, 2, 23, ...$

The $n^{th}$ superior highly composite number is the product of the first $n$ primes in this sequence.

What I would like to know is where do these primes come from?

Is there a formula which directly gives what is the $n^{th}$ term in this sequence? Or some other kind of relation?

At first I thought that the $n^{th}$ term in this sequence was the smallest prime $p$ such that $p^{a+1}$ is the smallest as possible, where $a$ is the number of times $p$ has already occurred in the sequence.

This correctly predicts the first $4$ terms: $2, 3, 2, 5$

But then it predicts that the next few terms are $7, 2, 3$ instead of $2, 3, 7$

So that's clearly not the answer.

a natural number which has more divisors than any other number scaled relative to the number itselfmean? Whatever this would mean, it sounds that there is at most one. $\endgroup$ – Włodzimierz Holsztyński Oct 27 '14 at 19:45