Yes! I was just in the middle of doing this in a sage notebook!
Good thinking :)
I have to think some mathematician had already done this for like every pattern they could think of but ya never know. Never hurts to try... As long as you don't delude yourself that is.
update:
Okay so the tricky thing here is that in order to naively generate the divisors (and sum over them), you'd have to consider butt-tons of combinations of prime factors, including many, many, many repeated ones.
So finding divisors given a list of factors scales very rapidly.
It's really fun to take shots at these hard problems. It's like any way you attack them they're hard, even when you don't intuitively expect it.
Good thinking :)
I have to think some mathematician had already done this for like every pattern they could think of but ya never know. Never hurts to try... As long as you don't delude yourself that is.
update: Okay so the tricky thing here is that in order to naively generate the divisors (and sum over them), you'd have to consider butt-tons of combinations of prime factors, including many, many, many repeated ones.
So finding divisors given a list of factors scales very rapidly.
It's really fun to take shots at these hard problems. It's like any way you attack them they're hard, even when you don't intuitively expect it.