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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 323-329 |
| Number of pages | 7 |
| Journal | Lithuanian Mathematical Journal |
| Volume | 61 |
| Issue number | 3 |
| Early online date | Jul 1 2021 |
| DOIs | |
| State | Published - Jul 2021 |
Keywords
- Hardy–Ramanujan inequality
- shifted primes
- sieves
ASJC Scopus subject areas
- General Mathematics
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