Problem Statement
Is the sum\[\sum_{n} \mu(n)^2\frac{n}{2^n}\]irrational?
Categories:
Irrationality
Progress
In [Er88c] Erdős makes the stronger conjecture that any infinite subseries over squarefree numbers is also irrational.This strong conjecture is true, and was proved by Chen and Ruzsa [ChRu99].
Source: erdosproblems.com/259 | Last verified: January 14, 2026