TR-MO 2019 Problem 2

Let $d(n)$ denote the number of divisors of a positive integer $n$ . If $k$ is a given odd number, prove that there exist an increasing arithmetic progression in positive integers $(a_1,a_2,\ldots a_{2019})$ such that $gcd(k,d(a_1)d(a_2)\ldots d(a_{2019})) =1$