A problem of Erd\H{o}s and Pomerance \cite{ErPo80}, who proved\[(2/\sqrt{e}+o(1))n\left(\frac{\log n}{\log\log n}\right)^{1/2}\leq f(n)\leq (1.7398\cdots+o(1))n(\log n)^{1/2}.\]In \cite{Er92c} Erd\H{o}s offered 2000 rupees for an asymptotic formula; for uniform comparison across prizes I have converted this using the 1992 exchange rates.

See also [711].


References


[Er92c] Erd\"{o}s, P., Some of my forgotten problems in number theory. Hardy-Ramanujan J. (1992), 34-50.

[ErPo80] P. Erd\H{o}s and C. Pomerance, Matching the natural numbers up to $n$ with distinct multiples of another interval. Indigationes Math. (1980), 147-151.