Recreational Programming (RecPro) is the discipline that encourages the study of computer programming through ludic problems. Problems that are typically studied within this discipline are similar to those of Recreational Mathematics (RecMat), which sometimes leads to the confusion of these two disciplines. The objective for RecPro is to write programs, while RecMat practitioners can use these programs to state (and prove if possible) conjectures about the solution. This interaction leads to a mathematical quality production. In an educational framework, problems in elemental number theory (those that are formulated with a basic knowledge of arithmetic) are very interesting, leading to the revision of classical unsolved problems. One of these problems is the general form of Zumkeller numbers (those natural numbers as such that their positive divisors can be divided into two disjoint sets with an equal sum). Writing programs by using a programming language that is close to mathematical notation (e.g. Haskell) is the first step to solving the problem, since it is possible to easily write simple and elegant programs so close to the description of the problem that proving their correctness is straightforward. (Contains 2 tables, 1 figure and 5 notes.)