On integers whose number of prime divisors belongs to a given residue class

摘要

We consider positive integers whose number of prime divisors is congruent to l modulo k. In this case, the calculation of prime divisors can be made either with or without taking into account the multiplicity, and the divisors themselves can be subjected to the additional requirement of belonging to some special set. We show that for k = 3, the distribution pattern of these numbers, in dependence on the value of l, differs fundamentally from that in the case k = 2, which was studied earlier.