NMC 2020 Problem 1

For a positive integer $n$ , denote by $g(n)$ the number of strictly ascending triples chosen from the set $\{1, 2, ..., n\}$ . Find the least positive integer $n$ such that the following holds:The number $g(n)$ can be written as the product of three different prime numbers which are (not necessarily consecutive) members in an arithmetic progression with common difference $336$ .