Distribution of numbers in the multiplication table

[BrianSoddingBoru4]

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

OK, well, prime numbers become more and more rare the numbers you are looking at get bigger. And, since prime numbers can't be found in an n*n multiplication table except in the interval <1,n], one could as well expect there to be more numbers in the multiplication table in higher intervals, rather than in lower intervals (there will be more prime numbers in lower intervals).
Furthermore, why would somebody expect there to be short intervals of growth in the distribution function, ones that my web-app ( https://flatassembler.github.io/multiplication.html ) draws red?

It’s got nothing to do with prime numbers (well...a little bit to do with prime numbers). It has to with there being fewer factors of larger products in the 1-10 integer range.

Let’s look at the number 60. Factors for this are 1,2,3,4,5,6,10,12,15,20,30 and 60. But on a 10x10 table, you can only include 6 and 10 (the others are disqualified because you need a multiplier greater than ten to reach 60). This necessarily result in fewer products in the high end of the table.

Boru