Abstract
For any prime number p, let J(p) be the set of positive integers n such that the numerator of the nth harmonic number in the lowest terms is divisible by this prime number p. We consider an extension of this set to the generalized harmonic numbers, which are a natural extension of the harmonic numbers. Then, we present an upper bound for the number of elements in this set. Moreover, we state an explicit condition to show the finiteness of our set, together with relations to Bernoulli and Euler numbers.
| Original language | English |
|---|---|
| Pages (from-to) | 933-955 |
| Number of pages | 23 |
| Journal | Bulletin of the Korean Mathematical Society |
| Volume | 60 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Jul 2023 |
Bibliographical note
Publisher Copyright:© 2023 Korean Mathematical Society.
Keywords
- generalized harmonic numbers
- Harmonic numbers
- p-adic valuation