Assignment: #ProperDivisors Due: 09/02/02018 Points: 4

### Specification

Copy the program ProperDivisors.java to your computer and implement the static method named process(). The TBI (To Be Implemented) method comment block documents the functionality of the process().

The inputs used by this program are defined in an int[] defined in the main() method. Each element of the array is passed to the process() method. The process() method functions as follows for each input n.

• if n is prime, then print it is prime and return
• print a count of n's proper divisors
• all of the proper divisors of n
• the sum of the proper divisors of n
• if n is perfect, abundant, or deficient
• if n is refactorable
• if n is square-free

The following definitions were copied from Wikipedia.org...

```   "A refactorable number or tau number is an integer n that is
divisible by the count of its divisors."

"In number theory, an abundant number or excessive number
is a number for which the sum of its proper divisors is
greater than the number itself."

"Numbers whose sum of proper factors equals the number itself
are called perfect numbers, while numbers whose sum of proper
factors is less than the number itself are called deficient numbers."

"In mathematics, a square-free integer (or squarefree integer) is
an integer which is divisible by no perfect square other than 1."
```
##### The Program's Output

The output of the program must match the following. {output file}

```205 (3 proper divisors)
...proper divisors: 1,5,41,
...deficient (sum: 47; ratio: 0.22926829268292684)
...not refactorable
...square-free
86268 (47 proper divisors)
...proper divisors: 1,2,3,4,6,7,12,13,14,21,26,28,39,42,52,78,79,84,91,
156,158,182,237,273,316,364,474,546,553,948,1027,
1092,1106,1659,2054,2212,3081,3318,4108,6162,6636,
7189,12324,14378,21567,28756,43134,
...abundant (sum: 164612; ratio: 1.90814670561506)
...not refactorable
...not square-free
12 (5 proper divisors)
...proper divisors: 1,2,3,4,6,
...abundant (sum: 16; ratio: 1.3333333333333333)
...refactorable
...not square-free
37 is prime
480 (23 proper divisors)
...proper divisors: 1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,80,
96,120,160,240,
...abundant (sum: 1032; ratio: 2.15)
...refactorable
...not square-free
540540 (191 proper divisors)
...proper divisors: 1,2,3,4,5,6,7,9,10,11,12,13,14,15,18,20,21,22,26,27,
28,30,33,35,36,39,42,44,45,52,54,55,60,63,65,66,70,
77,78,84,90,91,99,105,108,110,117,126,130,132,135,
140,143,154,156,165,180,182,189,195,198,210,220,231,
234,252,260,270,273,286,297,308,315,330,351,364,378,
385,390,396,420,429,455,462,468,495,540,546,572,585,
594,630,660,693,702,715,756,770,780,819,858,910,924,
945,990,1001,1092,1155,1170,1188,1260,1287,1365,
1386,1404,1430,1485,1540,1638,1716,1755,1820,1890,
1980,2002,2079,2145,2310,2340,2457,2574,2730,2772,
2860,2970,3003,3276,3465,3510,3780,3861,4004,4095,
4158,4290,4620,4914,5005,5148,5460,5940,6006,6435,
6930,7020,7722,8190,8316,8580,9009,9828,10010,10395,
12012,12285,12870,13860,15015,15444,16380,18018,
19305,20020,20790,24570,25740,27027,30030,36036,
38610,41580,45045,49140,54054,60060,77220,90090,
108108,135135,180180,270270,
...abundant (sum: 1717380; ratio: 3.1771561771561774)
...not refactorable
...not square-free
128 (7 proper divisors)
...proper divisors: 1,2,4,8,16,32,64,
...deficient (sum: 127; ratio: 0.9921875)
...refactorable
...not square-free
61 is prime
314159265 (47 proper divisors)
...proper divisors: 1,3,5,7,9,15,21,35,45,63,105,127,315,381,635,889,
1143,1905,2667,4445,5715,7853,8001,13335,23559,
39265,40005,54971,70677,117795,164913,274855,353385,
494739,824565,997331,2473695,2991993,4986655,
6981317,8975979,14959965,20943951,34906585,44879895,
62831853,104719755,
...deficient (sum: 313155423; ratio: 0.9968046716686837)
...not refactorable
...not square-free
2018 (3 proper divisors)
...proper divisors: 1,2,1009,
...deficient (sum: 1012; ratio: 0.5014866204162537)
...not refactorable
...square-free

```