To arrange the sentences in a logical order, we start by identifying relationships and transitions:
C. This introduces the "squatters", explaining who they are.
B. This sentence continues about the squatters' land, comparing its liveliness.
D. Adds detail about the cultivation on the squatters' land with "sweet potatoes".
E. Describes what else grows on the land, "beans ripened in the fields".
The coherent sequence of sentences is therefore: CBDE.
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: