  Much recent progress has been made concerning the probable existence of Odd
Perfect Numbers, forming part of what has come to be known as Sylvester's Web
Of Conditions. This paper proves some results concerning certain properties of
the sums of reciprocals of the factors of odd perfect numbers, or, in more
technical terms, the properties of the sub-sums of \sigma_{-1} (n). By this
result, it also establishes strong bounds on the prime factors of odd perfect
numbers using the number of distinct prime factors it may possess.
