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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?

 Nov 2, 2018
 #1
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n =110 = 2 x 5 x 11
a=2, b=5, c=11
110^((3*2 + 5)/11)=110^(11/11)=110
GCD [2, 5, 11] =1
a + b + c =2 + 5 + 11 = 18

Note: With 2 as the first factor, many n will meet the restrictions given in the question.

Examples: 2, 7, 13 =182,  2, 11, 17 =374,  2, 13, 19 =494,   2, 17, 23 =782,  2, 23, 29 =1,334......etc.

 Nov 2, 2018
edited by Guest  Nov 2, 2018
 #2
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I don't think you understood the question, a b and c don't have to be factors of n, and x is the number of proper positive factors of n, not the number of prime factors of n.

Guest Nov 2, 2018

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