Browsing by Author "Luca, Florian"
Now showing items 15 of 5

On integers for which the sum of divisors is the square of the squarefree core
Broughan, Kevin A.; De Koninck, JeanMarie; 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 multiplyperfect 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.
Coauthors for Florian Luca
Florian Luca has 9 coauthors in Research Commons.