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

unreviewedOpen. Worked here; no verified result yet.

number theory · solved · formalized (Lean) · 0 attempts

machinery: irrationality-of-series,prime-distribution,Hardy-Littlewood,Schinzel-Hypothesis-H,arithmetic-function-omega

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Formal proof

AMS 11 · textbook (literature)

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

OEIS1

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