On the Sum-of-digits Function over k-free Integers

Let sb(n) denote the sum-of-digits function in base (b ≥ 2) of the integer n. The aim of this work is to address a question proposed by Gelfond in 1967/1968. Specifically, we prove that sum-of-digits function of k-free integers of a monomial is equidistributed in arithmetic progressions.