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Is \[\sum_{n\geq 2}\frac{\omega(n)}{2^n}\] irrational? (Here $\omega(n)$ counts the number of distinct prime divisors of $n$.)
#69
:
[ErGr80]
[Er90]
[Er97f]
number theory
,
irrationality
Erdős
[Er48]
proved that $\sum_n \frac{d(n)}{2^n}$ is irrational, where $d(n)$ is the divisor function.
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