Erdős problem 250 · problems.science

Is $\sum_{n=1}^\infty \frac{\sigma(n)}{2^n}$ irrational? Here $\sigma(n)$ is the sum of divisors function.

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FormalConjectures/ErdosProblems/

250.lean

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Is $\sum_{n=1}^\infty \frac{\sigma(n)}{2^n}$ irrational? Here $\sigma(n)$ is the sum of divisors function.

The answer is yes, as shown by Nesterenko [Ne96].

[Ne96] Nesterenko, Yu V., _Modular functions and transcendence questions_, Mat. Sb. 187 *9* (1996), 1319--1348.

FormalConjectures/ErdosProblems/250.leanErdos250.erdos_2501 lineExact file

1(∀ (x : ℝ), HasSum (fun n => ↑((ArithmeticFunction.sigma 1) n) / 2 ^ n) x → Irrational x) ↔ True

SolvedStatement only, no proof