Do $\lambda(n)$ and $\pi(n)$ coincide infinitely often?

Question

Let $\pi(n)$ be the prime-counting function and $\lambda(n)$ the Carmichael-function.

Does $$\pi(n)=\lambda(n)$$ hold for infinite many positive integers $n$ ?

I have no idea for an approach other than just brute force. The solutions I got so far :

2 3 4 10 14 39 124 322 365 1086 3283 5205 16978 41899 53774 64730 64850 157165 481476 881787 1207317 3523898 9559815

Answer 1

I can't prove if there exists infinite matches.

However, one can find large solutions $\lambda(n) = \pi(n)$ by considering an integer ratio $r \approx \Large \frac{n}{\pi(n)}$. Chances are good to find $rq$ with $q$ is either a prime or a semi-prime, such that $\lambda(rq) = \pi(rq)$.

Let us consider $r = 42$. To find $n$, the Riemann $R(x)$ function is a good way to approximate:

$\Large \frac {n}{\pi(n)}$$\approx 42 \ $ with $\ n \approx 4.84777065654 \cdot 10^{18}$

Searching in that range the exact value for $\pi(n)$ has only to be determined once, then the primes within that range can be counted. $\lambda(n)$ has only to be calculated if $n$ is a multiple of $42$.

After all, six solutions can be spotted in this range:

$$\lambda(n) = \pi(n) = m$$

        n                       m
==========================================

4847770656544884894     115423110870116304

4847770656544922694     115423110870117204

4847770656544965702     115423110870118230

4847770656544978806     115423110870118542

4847770656544979562     115423110870118560

4847770656544980906     115423110870118590