Erdős problem 69 · problems.science

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

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2 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

69.lean

Retained formal statement2 of 2

Tao observed that erdos_69 is a special case of erdos_257, since $\sum_{n\geq 2}\frac{\omega(n)}{2^n} = \sum_p \frac{1}{2^p - 1}.$

FormalConjectures/ErdosProblems/69.leanErdos69.erdos_69.variants.specialisation_of_erdos_2572 linesExact file

1have A := {n | Nat.Prime n};2∑' (n : ℕ), ↑(ArithmeticFunction.cardDistinctFactors (n + 2)) / 2 ^ (n + 2) = ∑' (p : ↑A), 1 / (2 ^ ↑p - 1)

SolvedStatement only, no proof