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If $\tau(n)$ counts the divisors of $n$ then let \[f(n)=\sum_{1\leq k\leq n}\tau(2^k-1).\] Does $f(2n)/f(n)$ tend to a limit?
#893
:
[Er98]
number theory
,
divisors
Erdős
[Er98]
says that 'probably there is no simple asymptotic formula for $f(n)$ since $f(n)$ increases too fast'.
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