  Let D(e) denote the weighted Dynkin diagram of a nilpotent element $e$ in
complex simple Lie algebra $\g$. We say that D(e) is divisible if D(e)/2 is
again a weighted Dynkin diagram. (That is, a necessary condition for
divisibility is that $e$ is even.) The corresponding pair of nilpotent orbits
is said to be friendly. In this note, we classify the friendly pairs and
describe some of their properties. We also observe that any subalgebra sl(3) in
$\g$ determines a friendly pair. Such pairs are called A2-pairs. It turns out
that the centraliser of the lower orbit in an A2-pair has some remarkable
properties. Let $Gx$ be such an orbit and $h$ a characteristic of $x$. Then $h$
determines the Z-grading of the centraliser $z=z(x)$. We prove that $z$ is
generated by the Levi subalgebra $z(0)$ and two elements in $z(1)$. In
particular, (1) the nilpotent radical of $z$ is generated by $z(1)$ and (2)
$x\in [z,z]$. The nilpotent elements having the last property are called
reachable.
