Divisor Count Function of Power of Prime

Theorem
Let $$n = p^k$$ be the power of a prime number $$p$$.

Let $$\tau \left({n}\right)$$ be the tau function of $$n$$.

That is, let $$\tau \left({n}\right)$$ be the number of positive divisors of $$n$$.

Then $$\tau \left({n}\right) = k + 1$$.

Proof
The divisors of $$n = p^k$$ are $$1, p, p^2, \ldots, p^{k-1}, p^k$$.

There are $$k + 1$$ of them.

Hence the result.