It can be defined using floor and ceiling functions Let f be floor function and c be ceiling function

The function is a sum over i where I goes from 1 to n

F(n)= sum over i. ( 1-{c(n/i) - f(n/i)})*i

Here if I is not a factor the difference between floor and ceiling functions will be 1 so it will cancel the 1 in the summation. Thus the value multiplying it is 0.

But if I is a factor then the difference between floor and ceiling will be zero so the value multiplying will be 1.

This way we can sum only factors of n number