Bulletin of the Korean Mathematical Society (대한수학회보)

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ON THE p-ADIC VALUATION OF GENERALIZED HARMONIC NUMBERS

  • Cagatay Altuntas (Department of Mathematics Engineering Faculty of Science and Literature Istanbul Technical University)
  • Received : 2022.06.10
  • Accepted : 2022.10.11
  • Published : 2023.07.31
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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.

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Acknowledgement

We are grateful to the referee for the comments which improved the presentation and quality of the paper.

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