Both prime numbers and highly divisible numbers have a common characteristic: divisibility. The former are divisible by as few lower numbers as possible, and the latter by as many as possible, like two poles on a scale. I'm interested into fitting all the other non-prime and non-highly-divisible whole numbers into such a scale too.
Any suggestions for creating a formula that translates whole numbers to the range of
[0,1], where prime numbers result in
0 and highly divisible numbers in
1, and all the other numbers in between?
Have there already been attempts to do this?