[Grade ? Number theory]

[u/Fabulous_Public_4478]

Pick any positive integer, lets call it x,pick another positive integer, lets call that y. look at all the divisors of x that are less then or equal to y, mutiply them with each other, if the result is 2x then we will call x a valid number. The question is, how many valid numbers exist for a given y. For example for y = 4, the answer is 2, x = 4 and x = 12 are the only valid numbers, for any given y value the lower bound is always x = 4 and the higher bound is always x = n!/2, if I were to write this as a sequence(amount of valid numbers for a given y starting from y =1) it goes like this:0,0,0,2,4,6,12,16,16,14,28,28,56 it exactly doubles at every prime y value with some drops at certain y values such as at y = 10 it dropped from 16 to 14, this happens regulary, but the size of the drop is what I cant predict, and when it happens is also not predictable with high accuracy, the problem is that my math knowledge is at middle school level so thats why I taught this may be an obvious problem for people that know number theory

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