What does $p^\alpha\| n$ mean?

Question

What does $p^\alpha\| n$ mean ? I saw this in Euler totient function, $$\varphi(n)=\prod_{p^\alpha\| n}p^\alpha(p-1).$$

Answer 1

It means that $p^{\alpha}\mid n$ but $p^{\alpha+1}\nmid n$.

For example. $2^2\mid 12$ but $2^3\nmid 12$. Hence $2^2\|12$

Answer 2

In that context it's a bit of an abuse of notation because it involves a condition on both alpha and p, not only on the power. It means p^alpha divides n but no larger power does.