Because of inflation, Santa can’t afford buying gifts for all children this year. He decided to divide his ordered list of good children into those who will get a gift and those who won’t. To be as fair as possible, he came up with the following (seemingly random) rule: ”Each child has its own number on my list. If $n$ is a positive integer which satisfies $$\tau (nk) \le k \cdot \tau (n)$$for all positive integers $k \ge 2$, then the $n^{th}$ child from my list will get a gift. ” Characterize all positive integers $n$ such that the $n^{th}$ child from the list gets a gift this year. Note: $\tau (n)$ denotes the number of positive divisors of $n$.