# divisor sum of an arithmetic function

Given an arithmetic function $f:\mathbb{Z}^{+}\rightarrow\mathbb{C}$, the divisor sum $F$ of $f$ is defined by

 $F(n)=\sum\limits_{d\mid n}f(d)\text{,}$ (1)

where the summation runs over all positive divisors $d$ of $n$.

Title divisor sum of an arithmetic function DivisorSumOfAnArithmeticFunction 2013-03-22 17:07:31 2013-03-22 17:07:31 azdbacks4234 (14155) azdbacks4234 (14155) 10 azdbacks4234 (14155) Definition msc 11A25 Divisibility ArithmeticFunction MultiplicativeFunction divisor sum