The board / number theory / #249
Erdős Problem #249
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Is \[\sum_{n} \frac{\phi(n)}{2^n}\] irrational? Here \(\phi\) is the Euler totient function.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/249.Prizenone
Topicsnumber theory, irrationality
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA256936
Original pageerdosproblems.com/249
Attempts
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