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The article discusses the study conducted to examine the reciprocal sum as a knowledge metric and also discusses its mathematical theory, computation and perfect numbers. Topics discussed include long and intimate connection of reciprocal sums with the number theory, using Euler's theorem for getting the better results of sum of reciprocals, and using partial summation as a powerful and versatile method for estimating the reciprocal sums.

Two numbers m and n are considered amicable if the sum of their proper divisors, s( n) and s( m), satisfy s( n) == m and s( m) == n. In 1981, Pomerance showed that the sum of the reciprocals of all such numbers, P, is a constant. We obtain both a lower and an upper bound on the value of P. [ABSTRACT FROM AUTHOR]