IMC 2005 — Keystage 3 (IWYMIC) — team Question 10

Find all positive integers $a_0\gt a_1\gt \cdots\gt a_n\gt 1$ satisfying $$\left(1-\frac1{a_1}\right)+\cdots+\left(1-\frac1{a_n}\right)=2\left(1-\frac1{a_0}\right).$$