Problem #249: Is\[\sum_n \frac{\phi(n)}{2^n}\]irrational?

Is\[\sum_n \frac{\phi(n)}{2^n}\]irrational? Here $\phi$ is theEuler totient function.

SOLVED

Problem Statement

Is\[\sum_n \frac{\phi(n)}{2^n}\]irrational? Here $\phi$ is the Euler totient function.

Categories: Number Theory Irrationality

The decimal expansion of this sum is A256936 on the OEIS.

Source: erdosproblems.com/249 | Last verified: January 14, 2026