Let $C_n$ be the $n$-th Carmichael-number and $$r:=\sum_{j=1}^{\infty} \frac{1}{C_j}$$
If we stop at the last Carmichael-number below $10^{16}$ ,we get $$0.0047065376661376\cdots $$ as an approximation.
How accurate will this approximation of $r$ be ? I assume this sum will converge although I have not rigorously proven it yet.
The bounds given in Wikipedia or Mathworld for the number of Carmichael-numbers below some given number $n$ are not very suitable for an estimate (not very tight and not even very concrete). What else can I do ?
Theorem: The sum $r$ of the reciprocals of the Carmichael numbers satisfies $$ 0.004706<r<27.8724. $$ For a proof see here. It seems that your value is rather accurate, but I haven't seen a proof.