A four-part trilogy

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

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

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

Let BB be the maximum value of f(n)n\dfrac{f(n)}{n} for n1000.n \le 1000.

Let CC be the maximum value of f(n)f(n) for n1000.n \le 1000.

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

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

This is my official (and somewhat belated) 1000 follower question.

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