With the power of Scribd I can now upload the cool Mathematica work I've done to supplement some of my old posts. Below there are two very long tables with data relating to Richey Numbers, and a couple of extensions.

The first table consists of all the numbers that can be written as the sum of two squares, their prime factorizations, their generators (what squares Mathematica added to get the number) and how many distinct ways they can be written as the sum of two squares. The second table has the same information, only it looks at the sum of two cubes, not two squares. The right column is the one that tells us how many ways that number can be written as the sum of two squares or cubes. That column tells me what numbers to look at- for the first table, those that have a value of 3 or greater are interesting because I've already generalized those that can be written in two or one ways as the sum of two squares. The second table has red in the right column when the value is greater than one, but I still haven't generalized the set of numbers that can be written in one way as the sum of two cubes, let alone two ways. Finally, the green in the left hand column occurs whenever the number in question is a prime or a power of a prime- I noticed some interesting trends among those types of numbers. See what trends you can find, and if you do see something interesting, write a comment!

Sum of Two Powers Table