  For n>1, let G(n)=\sigma(n)/(n log log n), where \sigma(n) is the sum of the
divisors of n. We prove that the Riemann Hypothesis is true if and only if 4 is
the only composite number N satisfying G(N) \ge \max(G(N/p),G(aN)), for all
prime factors p of N and all multiples aN of N. The proof uses Robin's and
Gronwall's theorems on G(n). An alternate proof of one step depends on two
properties of superabundant numbers proved using Alaoglu and Erd\H{o}s's
results.
