ON THE MEAN VALUE OF THE INDEX OF COMPOSITION OF AN INTEGER II

For each integer n ≥ 2, let [Formula: see text] be the index of composition of n, where γ(n) ≔ ∏ p∣n p. The index of composition of an integer measures the multiplicity of its prime factors. In this paper, we obtain a new asymptotic formula of the sum ∑ n≤x λ -k (n). Furthermore, we improve the error term under the Riemann Hypothesis.