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?

MathCuber
Nov 2, 2018

#1**0 **

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.

Guest Nov 2, 2018

edited by
Guest
Nov 2, 2018