Abstract
We show that for every fixed l ∈ N, the set of n with nl|(2nn) has a positive asymptotic density cl and we give an asymptotic formula for cl as l → ∞. We also show that #{n ≼ x, (n, (2nn)) = 1} ∼ cx/ log x for some constant c. We use results about the anatomy of integers and tools from Fourier analysis. One novelty is a method to capture the effect of large prime factors of integers in general sequences.
Original language | English (US) |
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Pages (from-to) | 823-953 |
Number of pages | 131 |
Journal | Transactions of the American Mathematical Society |
Volume | 374 |
Issue number | 2 |
DOIs | |
State | Published - Feb 2021 |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics