We know from the Prime Number Theorem (PNT) that
$$\frac{1}{N}\sum_{n=1}^N \Lambda(n)= 1+ o(1),$$
where $\Lambda$ is von Mangoldt function. Now consider $ W \in \mathbb{N}$ and define
$$\tilde{\Lambda} (n) := \ \frac{\Phi(W)}{W} \ln(Wn+1) $$
if $Wn+1$ is prime and $0$ otherwise.$\Phi$ is the Euler function. I saw somewhere that by Dirichlet's famous theorem about primes in arithmetic progressions and the PNT, it can be proved that
$$\frac{1}{N}\sum_{n=1}^N \tilde\Lambda(n)= 1+ o(1).$$
Would anyone please introduce me some references to read the proof?