Let $x$ be an integer, $r(x)$ the reciprocal of the largest prime factor of $x$.
Let $f(n) = \sum_{k=1}^{n-1} r(k) r(n-k)$ for which $k$ and $(n-k)$ are coprime.
For $n = 3 \dots 10$, $f(n) = 1\ \ 0.6666\ \ 1.3333\ \ 0.4\ \ 1.2\ \ 0.419\ \ 1.342\ \ 0.761$
For example:
$f(5) = r(1) r(4) + r(2) r(3) + r(3) r(2) + r(4) r(1) = 1/2 + 1/2\ \ 1/3 + 1/3\ \ 1/2 + 1/2 = 1.3333$
Put $s(n) = \sum_{k=1}^{n}$ f(k)
Conjecture. $s(n)/n$ tends to a number $p$, where $0<p<1$ as $n\to\infty$.
$s(1000) = 0.7913$ x 1000