Define a function $f : \mathbb{N} \rightarrow \mathbb{Z}^{+} \cup \{0\}$ such that

$f(1) = 0, f(p) = 1$ for $p$ prime, and $f(mn) = mf(n) + nf(m).$

Let $A$ be the sum of all $n \lt 1,000,000$ such that $f(n) = n.$

Let $B$ be the maximum value of $\dfrac{f(n)}{n}$ for $n \le 1000.$

Let $C$ be the maximum value of $f(n)$ for $n \le 1000.$

Finally, let $D = f(1000) + f(42).$

Find $A + 2B + C + D.$