On Quotients of Values of Euler's Function on Factorials

  title={On Quotients of Values of Euler's Function on Factorials},
  author={Ayan Nath and Abhishek Kumar Jha},
Recently, there has been some interest in values of arithmetical functions on members of special sequences, such as Euler’s totient function φ on factorials, linear recurrences, etc. In this article, we investigate, for given positive integers a and b, the least positive integer c = c(a, b) such that the quotient φ(c!)/φ(a!)φ(b!) is an integer. We derive results on the limit of the ratio c(a, b)/(a + b) as a and b tend to infinity. Furthermore, we show that c(a, b) > a+ b for all pairs of… 

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