How many numbers below a product of first n primes P are coprime with P?

Question

Products of first primes are P1= 2; P2= 2*3=6; P3= 2*3*5=30; P4=2*3*5*7=210; etc.

Coprimes.
P1 : {1}
P2 : {1,5}
P3 : {1,7,11,13,17,19,23,29}

Coprime count.
P1: 1
P2: 2
P3: 8
Pn: Cn
What is the sequence of coprime count Cn?

Answer 1

Note that $C3= (2-1)(3-1)(5-1)$ This is not a coincidence. $\frac 12$ of the numbers are odd, $\frac 23$ do not have a factor $3$, and $\frac 45$ do not have a factor $5$. So $Cn$ is the product of one less than each prime up to the $n^{th}$