L

```
-- Prime-factorize a number. Runs in sqrt(n) time. "Naive" implementation as opposed to advanced "sieves".
return function(
n -- integer to factorize
)
local factors = {}
for factor = 2, n ^ 0.5 do
local count = 0
while n % factor == 0 do
count = count + 1
n = n / factor
end
if count > 0 then
factors[factor] = count
end
end
if next(factors) == nil then -- no factors: number is a prime (or 0 or 1)
factors[n] = 1
end
-- prime factorization as table `[factor] = count`; `{[1] = 1}` for `n=1`
return factors
end
```