On number of integers representable as a sum of unit fractions. II
Denote by \(N(n)\) the set of positive integers \(a\) representable in the form \[ a = \sum_{\nu=1}^n {\varepsilon_\nu \over \nu}, \text{ where } \varepsilon \in \{0, 1\}. \] Continuing his research [in \textit{H. Yokota}, Can. Math. Bull. 33, 235-241 (1990; Zbl 0656.10012)], the author proves rather sharp lower and upper estimates for the number of elements in \( N(n) \): For all sufficiently large \(n\), \[ \left( 1 - {5 \log\log n \over \log n} \right) \leq {\#\{N(n)\} \over \log n} < \left( 1 + {1 \over \log n} \right). \] In particular, \( \# \{N(n)\} \sim \log n \).
asymptotic formula for the number of integers representable as sums of unit fractions
scientific article; zbMATH DE number 1109643