Primes in the prime factorisation I saw another prime challenge coming by in PPCG, and I do love me some primes. Then I misread the introductory text, and wondered what the creative brains here had come up with.
It turns out the question posed was trivial, but I wonder if the same is true of the question I (mis)read:

\$6\$ can be represented by \$2^1\times3^1\$, and \$50\$ can be represented by \$2^1\times5^2\$.
Your task:
Write a program or function to determine how many distinct primes there are in this representation of a number.
Input:
An integer \$n\$ such that \$1 &lt; n &lt; 10^{12}\$, taken by any normal method.
Output:
The number of distinct primes that are required to represent the unique prime factors of \$n\$.
Test cases:
Input      Factorisation      Unique primes in factorisation representation
24         2^3*3^1            2 (2, 3)
126        2^1*3^2*7^1        3 (2, 3, 7)
8          2^3                2 (2, 3)
64         2^6                1 (2) (6 doesn't get factorised further)
72         2^3*3^2            2 (2, 3)
8640       2^6*3^3*5^1        3 (2, 3, 5)
317011968  2^11*3^5*7^2*13^1  6 (2, 3, 5, 7, 11, 13)
27         3^3                1 (3)

This is not an OEIS sequence.
Scoring:
This is code-golf, lowest score in bytes wins!
Mathematica, 39 bytes
Count[Union@@FactorInteger@#,_?PrimeQ]&amp;

Try it online!
thanks to Martin Ender (-11 bytes)