Claims

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1955_01_01_lambek_moser: Lambek and Moser (Canad. J. Math. 1955): a density criterion for n coprime to f(n), giving density 6/pi^2 for f(n) the integer part of n^{1/k} with k >= 2 an integer; refereed.

2002_09_01_delmer_deshouillers: Delmer and Deshouillers (Period. Math. Hungar. 2002): for every positive non-integer c, the integers n coprime to the integer part of n^c have density 6/pi^2; refereed.

2016_11_24_bergelson_richter: Theorem 1 of Bergelson and Richter (arXiv 2016, Springer 2017): for a Hardy-field f above log t log_4 t and strictly between consecutive powers of t, n and the integer part of f(n) are coprime with density 6/pi^2.

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