Euler's Product formula upside down

This model shows how if you put $1, 2, 2^2, 2^3, ...$, along one axis, $1,3, 3^2, 3^3, ...$ along another and $1, 5, 5^2, 5^3, ...$ along a third and then fill out the 3D table by multiplying everything, you end up getting all possible numbers made from 2s, 3s and 5s.

If you imagine this with a dimension for every prime number you get the formula $\prod{\sum{p^k}} = \sum{n}$

Pascal's triangle

Here is a Lego model of Pascal's Triangle.

Each number in the triangle is represented by a tower of its prime factors. By changing the order of the blocks you can make the divisibility properties easy to see. Here is the model with all the orange 7 blocks moved to the top.

The upside-down orange triangle shows the numbers that are divisible by 7.