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OPEN This is open, and cannot be resolved with a finite computation.
Is\[\sum_n \frac{\phi(n)}{2^n}\]irrational? Here $\phi$ is the Euler totient function.
Disclaimer: The open status of this problem reflects the current belief of the owner of this website. There may be literature on this problem that I am unaware of, which may partially or completely solve the stated problem. Please do your own literature search before expending significant effort on solving this problem. If you find any relevant literature not mentioned here, please add this in a comment.
The decimal expansion of this sum is A256936 on the OEIS.

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This page was last edited 28 September 2025.

External data from the database - you can help update this
Formalised statement? Yes
Related OEIS sequences: A256936

When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:

T. F. Bloom, Erdős Problem #249, https://www.erdosproblems.com/249, accessed 2025-11-16
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