(June 8, 2020 at 5:49 am)FlatAssembler Wrote:(June 8, 2020 at 5:06 am)BrianSoddingBoru4 Wrote: It's the nature of arithmetic. Not all numbers from 1-100 are the product of integers from 1-10.
I'm not sure why this is even a question.
Boru
Of course not all numbers from 1-100 are the product of integers from 1-10, but why aren't those numbers that are products evenly distributed? Furthermore, why is the distribution function mostly falling, but also has short intervals of growth?
Why SHOULD they be evenly distributed? As you get to larger and larger numbers, it takes larger and larger integers to multiply to produce those numbers. But you're only working with factors of 1-10. So, the higher the product, the less likely it is to be produced by multiplying just 1-10 by other integers from 1-10.
For example, lets look at two numbers, 30 and 94. The factors of 30 (that is, those integers that you can multiply to get 20) on a 10x10 multiplication table are 3,5,6, and 10. But for 94, the only factor on the same table is 2.
Boru
‘But it does me no injury for my neighbour to say there are twenty gods or no gods. It neither picks my pocket nor breaks my leg.’ - Thomas Jefferson
