Now showing items 1-5 of 5

  • On integers for which the sum of divisors is the square of the squarefree core

    Broughan, Kevin A.; De Koninck, Jean-Marie; K´atai, Imre; Luca, Florian (University of Waterloo, 2012)
    We study integers n > 1 satisfying the relation σ(n) = γ(n) ² , where σ(n) and γ(n) are the sum of divisors and the product of distinct primes dividing n, respectively. We show that the only solution n with at most four ...
  • On square values of the product of the Euler totient and sum of divisors functions

    Broughan, Kevin A.; Ford, Kevin; Luca, Florian (Polskiej Akademii Nauk, Instytut Matematyczny(Polish Academy of Sciences, Institute of Mathematics), 2012)
    If n is a positive integer such that ϕ(n)σ(n) = m² for some positive integer m, then m≤n. We put m = n - a and we study the positive integers a arising in this way.
  • On the Fürstenberg closure of a class of binary recurrences

    Broughan, Kevin A.; Luca, Florian (Elsevier, 2010)
    In this paper, we determine the closure in the full topology over Z of the set {un: n≥0}, where (un)n≥0 is a nondegenerate binary recurrent sequence with integer coefficients whose characteristic roots are quadratic units. ...
  • Perfect repdigits

    Broughan, Kevin A.; Sanchez, Sergio Guzman; Luca, Florian (American Mathematical Society, 2013)
    Here, we give an algorithm to detect all perfect repdigits in any base g>1. As an application, we find all such examples when g∈ [2, … ,333], extending a calculation from [2]. In particular, we demonstrate that there are ...
  • There are no multiply-perfect Fibonacci numbers

    Broughan, Kevin A.; Gonzalez, Marcos J.; Lewis, Ryan H.; Luca, Florian; Huguet, V. Janitzio Mejia; Togbe, Alain (Integers, 2011)
    Here, we show that no Fibonacci number (larger than 1) divides the sum of its divisors.