Prime factorize $ 284=2^2\cdot71 $. The sum of the proper divisors of $ 284 $ is \begin{align*} 1+2+2^2+71+2 \cdot 71 &= (1+2+2^2)(1+71)-284 \\ &= 220 \\ &= 2^2\cdot5\cdot11.\end{align*} Here we have used the observation that multiplying out $ (1+2+2^2)(1+71) $ by distributing yields an expression which is the sum of all $ 6 $ factors of $ 284 $. Applying this observation again, we find that the sum of the proper divisors of $ 220 $ is $$(1+2+2^2)(1+5)(1+11)-220=7\cdot 6\cdot 12-220=\boxed{284}.$$