Primes that are product of distinct primes plus one

Question

Primorial primes are the primes that are of the form $p_n \# \pm 1$, where $p_n \#$ is the product of first $n$ primes.

My doubt is follows:

Is there any special name or study for the primes of the form $2p_1p_2p_3\cdots p_n + 1$,where $p_1, p_2 \cdots p_n$ are distinct odd primes but not necessarily the first $n$ primes?

Answer 1

I think A039787 might be what you are looking for. On OEIS, they are called "Primes p such that p-1 is squarefree.". At first glance, there doesn't seem to be much research on these primes.

A075430 and A049097 are also relevant.