+586 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?
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
