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For Formula: see text, let Formula: see text denote the reciprocal sum up to x of numbers with k prime factors, counted with multiplicity. In prior work, the authors obtained estimates for Formula: see text, extending Mertens’ second theorem, as well as a finer-scale estimate for Formula: see text up to Formula: see text error for any Formula: see text. In this paper, we establish the limiting behavior of the higher Mertens constants from the Formula: see text estimate. We also extend these results to Formula: see text, and we comment on the general case Formula: see text.
Bayless et al. (Wed,) studied this question.