  This paper investigates the behaviour of one of the most famous Smarandache's
sequence given by A061076 on oeis. In particular we first study the behaviour
of two sequences (A061077, A061078) strictly connected with the main
Smarandache's sigma product of digits. We'll solve some open problems such as
the determination of an upper bound for these sequences (which hold for all
$n\in\mathbb{N}$) and the determination of a closed formula for each $a(n)$ and
$b(n)$. Then combining these results it will be possible to understand the
behaviour of the general sequence $c(n)$. Every result will be accompanied by
Wolfram Mathematica scripts examples in order to support our thesis.
