The product of the proper positive integer factors of n can be written as n^[(ax+b)/c], where x is the number of positive divisors n has, c is a positive integer, and the greatest common factor of the three integers a, b, and c is 1. What is a+b+c?


[Problem](/questions/problem_32)
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**There maybe many solutions to this question:**

 

**Here is just one of them:**

**182 =2 x 7 x 13.   This can be written as : 182^[(2*3 + 7) /  13] = 182^1 =182**

**The GCD of  2, 7, 13 = 1**

**Sum = 2 + 7 + 13 = 22**

**Note: By "positive integer factors", I took it to mean "Prime integer factors".**


Here are many solutions between 1 and 100, for a, b, c:  
 a=1; b=1;c=(6 + a) / b; if(c==1 and isprime(b), goto4, goto5);print2," ", a," ", b," = ",2*a*b; a++;if(a<100, goto2, 0);a=1;b++;if(b<100, goto2, discard=0;

 a   b    c          n  
 2   5   11     =  110  
 2   7   13    =  182  
 2   11   17   =  374  
 2   13   19  =  494  
 2   17   23  =  782  
 2   23   29  =  1334  
 2   25   31  =  1550  
 2   31   37  =  2294  
 2   35   41  =  2870  
 2   37   43  =  3182  
 2   41   47  =  3854  
 2   47   53  =  4982  
 2   53   59  =  6254  
 2   55   61  =  6710  
 2   61   67  =  8174  
 2   65   71  =  9230  
 2   67   73  =  9782  
 2   73   79  =  11534  
 2   77   83  =  12782  
 2   83   89  =  14774  
 2   91   97  =  17654

