Abstract
We establish an analog of the Hardy–Ramanujan inequality for counting members of sifted sets with a given number of distinct prime factors. In particular, we establish a bound for the number of shifted primes p + a below x with k distinct prime factors, uniformly for all positive integers k.
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30 December 2021
A Correction to this paper has been published: https://doi.org/10.1007/s10986-021-09550-9
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Ford, K. A Hardy–Ramanujan-type inequality for shifted primes and sifted sets. Lith Math J 61, 323–329 (2021). https://doi.org/10.1007/s10986-021-09523-y
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DOI: https://doi.org/10.1007/s10986-021-09523-y