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Let $n\geq 1$ and define $L_n$ to be the lowest common multiple of $\{1,\ldots,n\}$ and $a_n$ by \[\sum_{1\leq k\leq n}\frac{1}{k}=\frac{a_n}{L_n}.\] Is it true that $(a_n,L_n)=1$ and $(a_n,L_n)>1$ both occur for infinitely many $n$?
#291
:
[ErGr80]
number theory
,
unit fractions
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