Divisor sum identities
The purpose of this page is to catalog new, interesting, and useful identities related to number-theoretic divisor sums, i.e., sums of an arithmetic function over the divisors of a natural number n {\displaystyle n} , or equivalently the Dirichlet convolution of an arithmetic function f ( n ) {\displaystyle f(n)} with one: g ( n ) := ∑ d ∣ n f ( d ) . {\displaystyle g(n):=\sum _{d\mid n}f(d).} These identities include applications to sums of an arithmetic function over just the proper prime divisors of n {\displaystyle n} .