Sum Equal Product

There are many articles in re this issue on the Web, although many are restricted to special cases (e.g., John Cook’s sum of tangents = product of tangents), and even some involving mixed numbers.

There is one excellent article in re: sum equal product written by two Polish mathematicians which is replete with wonderful proofs that I am not sophisticated enough to understand. (Kurlandchick & Nowicki, Nov `98)

Actually, my question is quite straightforward. Is there a formula or some kind of algorithm that can show which sums of positive, unequal integers equal their products?

Falco