Problem Statement

An Abundant number is a number n for which the   sum of divisors   σ(n) > 2n, or,   equivalently,   the   sum of proper divisors   (or aliquot sum)       s(n) > n.

12   is abundant, it has the proper divisors     1,2,3,4 & 6     which sum to   16   ( > 12 or n);        or alternately,   has the sigma sum of   1,2,3,4,6 & 12   which sum to   28   ( > 24 or 2n).

Abundant numbers are common, though even abundant numbers seem to be much more common than odd abundant numbers. To make things more interesting, this task is specifically about finding   odd abundant numbers.

Let's start with the solution:

 [ 0 swap factors witheach + ] is sigmasum ( n --> n )

  0 -1 [ 2 + 
         dup sigmasum
         over 2 * over < iff
           [ over echo sp 
             echo cr  
             dip 1+ ]
         else drop 
         over 25 = until ]
  2drop
  cr 
  0 -1 
  [ 2 + dup sigmasum
    over 2 * > if [ dip 1+ ]
    over 1000 = until ]
  dup echo sp sigmasum echo cr 
  drop
  cr
  999999999
  [ 2 + dup sigmasum
    over 2 * > until ] 
  dup echo sp sigmasum echo cr