IMPROVED UPPER BOUNDS FOR ODD MULTIPERFECT NUMBERS

摘要

In this paper,we prove that, if N is a positive odd number with r distinct prime factors such that N | σ(N), then N < 2~(4~r-2~r) and N∏_(p|N) p < 2~(4~r) where σ(N) is the sum of all positive divisors of N. In particular, these bounds hold if N is an odd perfect number.