ISL 2016 N3

Define $P(n)=n^{2}+n+1$. For any positive integers $a$ and $b$, the set $$\{P(a), P(a+1), P(a+2), \ldots, P(a+b)\}$$ is said to be fragrant if none of its elements is relatively prime to the product of the other elements. Determine the smallest size of a fragrant set.