A fun pair of equivalences is 1 + 5 = 2 · 3 and 1 · 5 = 2 + 3. There are many like these, another one is 1 + 1 + 8 = 1 · 2 · 5 and 1 · 1 · 8 = 1 + 2 + 5. In general a product of n positive integers equals a sum of n positive integers, and vice versa.
In this challenge you must generate all such combinations of positive integers for an input n > 1, excluding permutations. You can output these in any reasonable format. For example, all the possible solutions for n = 3 are:
(2, 2, 2) (1, 1, 6) (1, 2, 3) (1, 2, 3) (1, 3, 3) (1, 1, 7) (1, 2, 5) (1, 1, 8)
The program that can generate the most combinations for the highest n in one minute on my 2GB RAM, 64-bit Intel Ubuntu laptop wins. If your answer uses more than 2GB of RAM or is written in a language I can not test with freely available software, I will not score your answer. I will test the answers in two weeks time from now and choose the winner. Later non-competing answers can still be posted of course.
Since it's not known what the full sets of solutions for all n are, you are allowed to post answers that generate incomplete solutions. However if another answer generates a (more) complete solution, even if their maximum n is smaller, that answer wins.
To clarify, here's the scoring process to decide the winner:
I will test your program with n=2, n=3, etc... I store all your outputs and stop when your program takes more than a minute or more than 2GB RAM. Each time the program is run for a given input n, it will be terminated if it takes more than 1 minute.
I look at all the results for all programs for n = 2. If a program produced less valid solutions than another, that program is eliminated.
Repeat step 2 for n=3, n=4, etc... The last program standing wins.