Linear sums on the floor function and three arithmetic functions (Q2090535)

In this paper, the author studies the sums \(\sum_{d|n}f(d)\) and \(\sum^\prime_{d\mid n}f(d)\), in terms of the floor function, where \(\sum^\prime\) means that the sum runs over the divisors of \(n\) such that \(n/d\) is odd. The author considers the cases \(f\) to be Jordan's totient function, the power function, and the Liouville function.