Let denote the number of prime divisors of counting multiplicity. One can show that for any positive integer and all , we have
with . Building on work of Kubota and Yoshida, we show that for and any , the error term is not for any .
"On the residue class distribution of the number of prime divisors of an integer." Nagoya Math. J. 202 15 - 22, June 2011. https://doi.org/10.1215/00277630-1260423