Problem Statement
What is the minimal value of $\lvert 1-\sum_{n\in A}\frac{1}{n}\rvert$ as $A$ ranges over all subsets of $\{1,\ldots,N\}$ which contain no $S$ such that $\sum_{n\in S}\frac{1}{n}=1$? Is it\[e^{-(c+o(1))N}\]for some constant $c\in (0,1)$?
Categories:
Number Theory Unit Fractions
Progress
It is trivially at least $1/[1,\ldots,N]$.Source: erdosproblems.com/311 | Last verified: January 14, 2026