For any integer $n\ge 1,$ the number of positive divisors of n is denoted by $d\left(n\right).$ Then for a prime p, $d\left(d\left(d\left(p^7\right)\right)\right)$ is 

d(n) = no of divisors

P = prime number

$\begin{array}{rcl}\left(\mathrm{d}\right(\mathrm{d}\left({\mathrm{p}}^7\right)\left)\right)& =& \mathrm{d}\left(\mathrm{d}\right(7+1\left)\right)\\ & =& \mathrm{d}\left(\mathrm{d}\right(2^3\left)\right) \\ & =& \mathrm{d}(3+1)\\ & =& \mathrm{d}\left(2^2\right)\\ & =& 2+1=3\end{array}$