I sadly can't think how to make this a challenge

Unfortunately I am not going to be able to give you an exact answer because the lists of prime numbers would take up more disk space than I have on my computer and doing it a few billion at a time would be very tedious

:(

And also because the fraction used as part of the solution would be several terabytes and I don't have that much RAM

a more efficient algorithm is needed!

Although wait, my approach is not actually the most efficient one at all

@RadvylfPrograms hmm.. can you read reader.elsevier.com/reader/sd/pii/…?

That's the reverse of what you're looking for

"free of prime factors >y"

it is sadly

If you're fine with running your computer for anywhere from 2 to 20 years and occasionally upgrading parts to keep up with moore's law, I've got a way to find an exact solution

:)

go on...

moore's law only applies to parallelisation now so it had better be multicore :)

Same thing I would've done with the list of primes, but with manual prime checking

For each prime number p up to y, you subtract complicated_function(p) from x

:)

I love complicated_function

I assume that's a single command in mathematica :)

complicated_function would just be x / p, except that since things like 6 would get subtracted twice (2 and 3), it needs to account for that

@RadvylfPrograms I asked on math.se and they don't know either yet :)

I don't think you're going to get an answer for something as big as a trillion

@RadvylfPrograms :( I hope someone clever will say something clever!

At least a good estimate

How good of an estimate are we talking

not sure it would give a good estimate though

One sig fig? Within 10%? How close does it need to be

I can get pretty close I think

@RadvylfPrograms as good as possible!

pretty close would be good

@RadvylfPrograms are you still working on this?

or writing an essay :)

Yep

cool!

how much math do you know?

@graffe Around 35 billion is my current estimate, give or take like 10 billion

I've found a somewhat interesting pattern though, which I'm going to investigate

Wait hold up miscalculation

Wait hang on now I'm getting a negative number

And that's a maximum

Oh I see why, and it's not something I can fix

I think I can think of a solution but I've spent way too much time on this

@RadvylfPrograms thanks so much!

It looks like I want a general version of Buchstab's function

@RadvylfPrograms en.wikipedia.org/wiki/Buchstab_function is so close!!

@RadvylfPrograms i love how the non-reply ping highlighting works sometimes

xD

@graffe Desmos, 43 bytes: f(x,y)=∑_{n=1}^xsign(∏_{k=2}^ymod(n,k)) Try It On Desmos!

45 bytes alternative that uses the 0^0 trick: f(x,y)=∑_{n=1}^x0^{∑_{k=2}^y0^{mod(n,k)}} Try It On Desmos!

(which is what i tried initially)

hi

@AidenChow that is intriguing! Is it really the exact answer?

@AidenChow the outputs look much too small

@graffe i compared it with the jelly answer that hyper gave, so if mines is wrong, so is his

@graffe they should be exact answers

^ this answer