  In 1973, Katona raised the problem of determining the maximum number of
subsets in a separating cover on n elements. The answer to Katona's question
turns out to be the inverse to the answer to a much simpler question: what is
the largest integer which is the product of positive integers with sum n? We
give a combinatorial explanation for this relationship, via Moon and Moser's
answer to a question of Erdos: how many maximal independent sets can a graph on
n vertices have? We conclude by showing how Moon and Moser's solution also
sheds light on a problem of Mahler and Popken's about the complexity of
integers.
