# standard sequential algorithm with polylog runtime?

At the Wikipedia article on time complexity, only a PRAM example is given for polylogarithmic time.

Let $T(n)$ denote the largest number of steps used by a machine to reach a final state on any input with size $n$ bits.

Is there a program for a standard sequential model of computation (e.g. a Turing machine or a sequential random-access machine), solving some natural problem, so that $T(n) \in \Theta((\log n)^k)$ for some fixed $k>1$?

Where each operation is $O\left(\log^kn\right)$ amortized/expected; I don't know if necessarily $\Theta\left(\log^kn\right)$:
There are also many algorithms with polylogarithmic factors; $\tilde {O}(\cdot)$ is notation that is used when hiding polylogarithmic factors. So $O\left(n\log^k n \right)\in\tilde {O}(n)$.