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

For each integer n ≥ 2, let be the index of composition of n, where γ(n) ≔ ∏p∣np. 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≤xλ-k(n). Furthermore, we improve the error term under the Riemann Hypothesis. [ABSTRACT FROM AUTHOR]