Erdős Problem 69

Theorem 69 · Erdős

Is $\sum_{n\geq 2}\frac{\omega(n)}{2^n}$ irrational? (Here $\omega(n)$ counts the number of distinct prime divisors of $n$ .)

Formal statement · Lean 4.lean

theorem erdos_69 : Irrational <| ∑' n, ω (n + 2) / 2 ^ (n + 2) := by
  sorry

Proof. sorry

Nobody has tried yet.