An idea used in the characterization of even perfect numbers is used, first, to derive new necessary conditions for the existence of an odd perfect number and, second, to show that there are no even 3-perfect numbers of the form 2 a M , where M is odd and squarefree and a Ä 718, besides the six known examples.

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Abstract. We say n ∈ N is perfect if σ(n)

In an Australian national batch-oriented computbr network, processing strategies have been investigated, using simulation, to give guidelines for management of the work load and to provide direction for measurement of the performance of the system under actual conditions. The nature of the conflicting interactions between computer resource utilization and transmission line requirements has been studied to provide the basis for an economic analysis to determine the most cost-effective processing strategy.