A Study on Factoriangular Numbers

Abstract

In this paper, we prove that there is no factoriangular number that is also factorial. An expression of factoriangular number explicitly in terms of triangular number is given. Bounds of the ratio of consecutive factoriangular number are given. It is shown that for n $\geq$ 5, there exists no $Ft_{n}$ which divides $Ft_{n+1}$. Patterns in factoriangular number modulo n is also observed. It is conjectuerd that there exists no factoriangular number that is a perfect square. It has also been conjectured that for n $\geq$ 6, 8n! + 1 is not a perfect square. A conjecture \cite{cas} that there is no factoriangular number that is an even perfect number is proved.