For some integer \(n\), let \(D_{n_1}=n\)  and for \(i>1\), let \(D_{n_i}\) be the sum of the factors of \(D_{n_{i-1}}\).

A number \(n\) is stupid if \(D_{n_1}\) and \(D_{n_2}\) are relatively prime.  For example, \(4\) contains the factors, \(1,\,2,\) and \(4,\) which add up to \(7.\) Thus, \(D_{4_1} = 4\) and \(D_{4_2} = 7\).  Since \(\gcd(4,\,7)=1\), it follows that \(4\) is stupid.

A number \(n\) is very stupid if for every pair \(x,\,y\) in \(\{D_{n_1},\,D_{n_2},\,D_{n_3}\}\), \(x\) and \(y\) are relatively prime. For example, \(D_{7_1} = 7,\,D_{7_2}=8,\) and \(D_{7_3}=15\), and so \(7\) is very stupid.

Similarly, a number \(n\) is very very stupid if for every pair  \(x,\,y\) in \(\{D_{n_1},\,D_{n_2},\,D_{n_3},\,D_{n_4}\}\), \(x\) and \(y\) are relatively prime.