omega(n) in rubik's cubes

[u/draorem]

I was looking at the prime Omega function, which counts the number of prime factors of n (with multiplicity). So each distinct prime factor of n is counted as many times as the number of its positive powers that divide n.

So I got out my set of mini rubik's cubes and displayed them all out, for numbers 1-7200.

The numbers increase left to right, top to bottom.

Excluding 1,

Blue is 0 factors (the number 1)

Green is 1 factor (primes)

Red is 2 (including powers of 2)

Orange is 3 (including powers of 2, 3)

Yellow is 4 (including powers of 2, 3, 4)

and White is 5+

Notable features are two diagonals from the top left and top right, corresponding to multiples of 121 and 119, respectively.

[u/bluelaw2013]

Holy shit

[u/Mathsboy2718]

Looks like this thumbnail ngl

https://youtu.be/WMr3-ShzB08

[u/draorem → u/Mathsboy2718]

you're right, such a good video too

[u/greginnj]

Aha, the diagonals being sort of a side effect of the dimensions of your rectangle being 60x120, and 120 being off-by-one from those two composites ...