What does this product converges to?

Question

Let $p\in[0,1]$.

I'm interested in computing

$$\lim_{n\to\infty}\prod_{i=1}^n(1-p^i)$$

Any thoughts?

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EDIT: As Kibble mentioned, this is the Euler function.

Also from Kibble: a simple upper bound is reached by ending the product early.

Can we derive a lower bound for $\phi(q)$?