Let g(n) be an arbitrary arithmetical function for which g(0)=0.Define j(n)=for n> 1 and f(1)=0,where is the standard factorisation of n.In thisi=1paper,the asymptotic formula for the sum given, where Ω(n) denotes the number oftotal prime factors of n.
On the Functions Denoting the Number of Prime Factors of a Natural Number. Acta Mathematica Sinica, Chinese Series, 1996, 39(5) https://doi.org/10.12386/A1996sxxb0084