For any integer $n \geq 1$, the number of positive divisors of $n$ is denoted by $d(n)$. Then, for a prime…
For any integer $n \geq 1$, the number of positive divisors of $n$ is denoted by $d(n)$. Then, for a prime $P, d\left(d\left(d(P)^7\right)\right)$ is equal to
$1$
$2$
$3$
$P$
Solution
Since, $d(n)$ represents number of the divisors of $n$.
$\begin{array}{rlrl}
& d\left(P^7\right) =8 \\
& d(8)= d\left(2^3\right) =4 \\
& d(4)= d\left(2^2\right) =3 \\
\therefore & d\left(d\left(d\left(P^7\right)\right)\right) =3
\end{array}$