The Sieve of Eratosthenes
Here is a simple script to produce Eratosthenes Sieve of Prime Numbers. Challenges to my students (and anyone else who wants to play along!):
1) Make the program more efficient. Hint - check the loops for numbers that might not need to be checked!
2) Use the logic that finds and enters factors into the list to make a similar sieve for Perfect, Abundant, and Defective numbers. What patterns show up.
3) Expand the sieve (smaller squares, longer loops!)
4) Factor trees and prime factorials? Can it be done in Scratch? Hmmmmm....