For every integer n, n* is defined as the sum of all the distinct

Question

For every integer n, n* is defined as the sum of all the distinct factors of n. Which of the following is equal to 10*?

A. 5*
B. 15*
C. 17*
D. 18*
E. 100*

Archit3110 · Answer

factors of 10 ; 2,5,10
sum ; 17
IMO c

saukrit · Answer

The factors of 10 are 1,2,5,10. The Sum= 18

IMO, the answer should be D

nick1816 · Answer

let  P= a^m * b^n * c^o  ........
where a,b and c are distinct primes
Sum of factor of P=  \frac{a^{m+1}- 1}{a-1} * \frac{b^{n+1}- 1}{b-1} * \frac{c^{o+1}- 1}{c-1}  ...
10=2*5
sum of factors of 10=  \frac{(2^2 -1)}{(2-1)} * \frac{(5^2 -1)}{(5-1)}= 3*6=18

sach24x7 · Answer

Guys i solved it this way.

Sum of factors of 10- 1+10+2+5= 18

Only 17 will give sum of factors 1+17= 18

Hope i’m correct.

Posted from my mobile device

brains · Answer

Hello  Bunuel  ,

Please correct me if i am wrong.

Distinct factors of 10 are 1,2,5,10 
Hence the sum should be 18.

However, the OA is given as C(which is 17). Am i missing something here?

Thank you

Bunuel · Answer

10* = the sum of all the distinct factors of 10 = 1 + 2 + 5 + 10 = 18.
17* = the sum of all the distinct factors of 17 = 1 + 17 = 18.

Option C shows 17 * , not 17. 
Option D shows 18 * , not 18.

Hope it's clear.

Kinshook · Answer

Given:  For every integer n, n* is defined as the sum of all the distinct factors of n.

Asked:  Which of the following is equal to 10*?

10 = 2*5
Distinct factors of 10 = {1,2,5,10}
Sum of distinct factors of 10 = 1+2+5+10 = 18
10* =18

Distinct factors of 17 = {1,17}
Sum of distinct factors of 17 = 1+17 = 18
17* =18
10* =18 = 17*

IMO C

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For every integer n, n* is defined as the sum of all the distinct

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For every integer n, n* is defined as the sum of all the distinct

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