Divisibility-preserving function

Definition

Suppose is an arithmetic function, i.e., is a function from the natural numbers to a commutative unital ring . We say that is divisibility-preserving if, whenever and are natural numbers such that divides , divides .

Note that whether a function is divisibility-preserving depends on what we consider the target ring.

Relation with other properties

Stronger properties

• Completely multiplicative function