Write a Java program $($called ETest$10)$ which reads in a single integer and prints whether or not that number in an Achilles number. You must produce input and output in the precise form shown below $($in the Example interaction$)$ and you must write and use the following public static functions as part of your solution:

void main$($ String$[]$ args$)$ which reads in a single number, and printed whether on not that number is an Achilles Number.

boolean isAchillesNumber $($ int number $)$ which returns whether or not the passed number is an Achilles number. An Achilles number is one which powerful but NOT a perfect power. The first Achilles numbers are $72,108,200,288.$

boolean isPerfectPower$($ int number$)$ which whether the passed number is a perfect power. An perfect power is a number which can be computed by raising some other number to a power. For example $8$ is a perfect power as it can be computed by raising $2$ to the power $3($i$.$e$.8=2^{**}{2}^{**}2).$ The first powerful numbers are $1,4,8,9,16,25,27,32.$

boolean isPowerful$($ int number$)$ which returns whether the passed number is a powerful number. An integer $n$ is called powerful if$,$ for every prime $p$ dividing evenly into $n,p^{**}p$ also divides evenly into $n.$ For example $8$ is a powerful number as the only prime which divides evenly into it is $2$ and $2**2=4$ which also divides evenly into $8.$ The first powerful numbers are $1,4,8,9,16,25.$

int$[]$ getPrimeFactors$($ int number$)$ which returns an array containing the prime factors of the passed number, in ascending order. E$.$g$.$

if passed $15$ it will return $[3,5],$ as $15=3^{**}5$ and $3$&$5$ are primes. if passed $28$ it will return $[2,2,7,$ as $28=2^{**}{2}^{**}7$ and $2$&$7$ are primes.

if passed $7$ it will return $[7],$ as $7$ is a prime already.

if passed any number $1,$ it will return null.

Example interaction $(3$ separate test runs, input shown in green bold$)$:

Enter any integer:

$72$

$72$ is an Achilles number.

Enter any integer:

$16$

$16$ is not an Achilles number.

Enter any integer:

$3\mathrm{.}14$

Error in input. You needed to supply integer values.