Problem #250: Is\[\sum \frac{\sigma(n)}{2^n}\]irrational?

Is\[\sum \frac{\sigma(n)}{2^n}\]irrational? (Here $\sigma(n)$ is the sum of divisors function.)

SOLVED

Problem Statement

Is\[\sum \frac{\sigma(n)}{2^n}\]irrational? (Here $\sigma(n)$ is the sum of divisors function.)

Categories: Number Theory Irrationality

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

This problem has been formalised in Lean as part of the Google DeepMind Formal Conjectures project.

Source: erdosproblems.com/250 | Last verified: January 14, 2026