Problem 148

Erdős Problem #148: declared status 'open'. Formalized: no. Let $F(k)$ be the number of solutions to$$1= \frac{1}{n_1}+\cdots+\frac{1}{n_k},$$where $1\leq n_1<\cdots<n_k$ are distinct integers. Find good estimates for $F(k)$. Current best: The lower bound is due to Konyagin [Ko14] and the upper bound to Elsholtz and Planitzer [ElPl21]. V., Double exponential lower bound for the number of representations of unity by Egyptian fractions. Prize: no. OEIS: A006585, A076393. Tags: number theory, unit fractions.