Type: Article

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

Luca, Florian; Young, Paul Thomas;

Abstract:

Let d(m) be the number of divisors of the positive integer m. Here, we show that if n is not an element of {3, 5}, then d(n!) is a divisor of n!. We also show that the only positive integers n such that d(F-n) divides F-n, where F-n is the nth Fibonacci number, are n is an element of {1, 2, 3, 6, 24, 48}.