Proof: Suppose n is a perfect number and d its proper divisor
. Let 1, [x.sub.2], [x.sub.3] ...
Abstract Let n be a positive integer, [p.sub.d](n) denotes the product of all positive divisors of n, [q.sub.d](n) denotes the product of all proper divisors
The three integers 19, 3 and 8 are all examples of what mathematicians refer to as 'deficient' in the sense that they are greater than the sum of their proper divisors
. (The proper divisors
of an integer n are those integers dividing evenly into n with the exception of n itself).
Our modification will consist of (1) summing all the divisors of n, not just the proper divisors
; (2) reversing the divisors before summing them--i.e., we'll use the srd(n) function.