On power values of sum of divisors function in arithmetic progressions

Let a > 1, b > 0 and k > 2 be any given integers. It has been proven that there exist infinitely many natural numbers m such that sum of divisors of m is a perfect kth power. We try to generalize this result when the values of m belong to any given infinite arithmetic progression an + b. We prove if a is relatively prime to b and order of b modulo a is relatively prime to k then there exist infinitely many natural numbers n such that sum of divisors of an + b is a perfect kth power. We also prove that, in general, either sum of divisors of an + b is not a perfect kth power for any natural number n or sum of divisors of an + b is a perfect kth power for infinitely many natural numbers n.