## Abstract

We show that for every fixed l ∈ N, the set of n with nl|(^{2}_{n}^{n)} has a positive asymptotic density cl and we give an asymptotic formula for cl as l → ∞. We also show that #{n ≼ x, (n, (^{2}_{n}^{n)}) = 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

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