One Half of a Primorial

Question

Is there a name for a half primorial? How should a half primorial be notated?

The first three primorials are 2,6, and 30. The first three half primorials are 1,3, and 15.

I have found that the half primorials are of great importance and need to know if there is any standard terminology or notation for them.

Answer 1

How should a half primorial be notated?

$\dfrac{p\#}2$

Is there a name for a half primorial?

No, there is no established term for this notion.