About the Non-Integer Property of Hyperharmonic Numbers

Abstract

It was proven in 1915 by Leopold Theisinger that the $H_n$ harmonic numbers are never integers. In 1996 Conway and Guy have defined the concept of hyperharmonic numbers. The question naturally arises: are there any integer hyperharmonic numbers? The author gives a partial answer to this question and conjectures that the answer is "no".

7 pages Accepted in Annales Univ. Sci. Budapest., Sect. Math