Abstract:
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 $k\geqslant3$, 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.
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