Erdős problem 69

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

Sources

The source's own material, retained exactly.

2 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

69.lean

Retained formal statement1 of 2

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

FormalConjectures/ErdosProblems/69.leanErdos69.erdos_691 lineExact file

1Irrational (∑' (n : ℕ), ↑(ArithmeticFunction.cardDistinctFactors (n + 2)) / 2 ^ (n + 2))

TextbookStatement only, no proof