Delmer and Deshouillers's coprimality density for n and [n^c]

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Updated Oct 7

Claim. F. Delmer and J.-M. Deshouillers, On the probability that $n$ and $[n^c]$ are coprime, Period. Math. Hungar. 45 (2002), no. 1--2, 15--20. Their abstract states that for every positive real $c$ that is not an integer, the set of integers $n$ coprime to $\lfloor n^c\rfloor$ has density $6/\pi^2$ , and it presents this as a conjecture of Moser, Lambek and Erdős. With $c=\alpha$ this is the statement of Problem 1149.

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Acceptance. Refereed: Periodica Mathematica Hungarica 45 (2002). The site's commentary credits Bergelson and Richter, not this paper. Bergelson and Richter's introduction cites it for the general case. The page name's date is the issue's month, September 2002; the day is unknown.

Linked from (4)

Problem 1149 Lambek and Moser's coprimality density for n and [n^{1/k}]Bergelson and Richter's coprimality density problems/integer_sequences/E1149/claims

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