Original scientific paper

https://doi.org/10.3336/gm.47.2.05

On the number of divisors of n! and of the Fibonacci numbers

Florian Luca ; Instituto de Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, México
Paul Thomas Young ; Department of Mathematics, College of Charleston, Charleston, SC 29424, USA

Abstract

Let d(m) be the number of divisors of the positive integer m. Here, we show that if n {3,5}, then d(n!) is a divisor of n!. We also show that the only positive integers n such that d(Fn) divides Fn, where Fn is the nth Fibonacci number, are n {1,2,3,6,24,48}.

Keywords

Divisors; factorials; Fibonacci numbers

Hrčak ID:

93943

URI

https://hrcak.srce.hr/93943

Publication date:

19.12.2012.

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