the maximum value for which combination of merge sort and insertion sort works more efficiently than standard merge sort?
Don't forget that big O notation hides constants. We want $nk + n\log(n/k)$ to be at most $Cn\log n$ for some constant $C&gt;0$. This means that $k + \log(n/k) \leq C \log n$, and so $k - \log k \leq (C-1)\log n$. You can check that this inequality holds (for some $C&gt;0$) if and only if $k = O(\log n)$.