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Let $a\geq 1, b\geq 0$ and $k\geq 2$ be any given integers. It has beenproven that there exist infinitely many natural numbers $m$ such that sum ofdivisors of $m$ is a perfect $k$th power. We try to generalize this result whenthe 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 $a$ isrelatively prime to $k$ then there exist infinitely many natural numbers $n$such that sum of divisors of $an+b$ is a perfect $k$th power. We also provethat, in general, either sum of divisors of $an+b$ is not a perfect $k$th powerfor any natural number $n$ or sum of divisors of $an+b$ is a perfect $k$thpower for infinitely many natural numbers $n$.

On Power Values of Sum of Divisors function in Arithmetic Progressions