  We consider the summatory function of the number of prime factors for
integers $\leq x$ over arithmetic progressions. Numerical experiments suggest
that some arithmetic progressions consist more number of prime factors than
others. Greg Martin conjectured that the difference of the summatory functions
should attain a constant sign for all sufficiently large $x$. In this paper, we
provide strong evidence for Greg Martin's conjecture. Moreover, we derive a
general theorem for arithmetic functions from the Selberg class.
