Jean-Marie De Koninck, Nicolas Doyon, "On a thin set of integers involving the largest prime factor function", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 639295, 8 pages, 2003. https://doi.org/10.1155/S016117120320418X
On a thin set of integers involving the largest prime factor function
For each integer , let denote its largest prime factor. Let does not divide and . Erdős (1991) conjectured that is a set of zero density. This was proved by Kastanas (1994) who established that . Recently, Akbik (1999) proved that . In this paper, we show that . We also investigate small and large gaps among the elements of and state some conjectures.
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