Solution
= Solution
For a positive integer $d$, define
$$
|\mathcal A_d|=\sum_{\substack{n\geq1\\d\mid n}}a_n.
$$
The sequence $\mathcal A$ has <sieve distribution> $(X,P_z,g,(r_d))$ when $g$ is a <multiplicative arithmetic function> on the squarefree divisors of $P_z$, with $0\leq g(p)<1$, and
$$
|\mathcal A_d|=Xg(d)+r_d
$$
for every $d\mid P_z$. The function $g(d)$ models the local density of divisibility by $d$, while $r_d$ is the remainder.