# Recursively* *divisible numbers

Number theory

## Recursively divisible numbers

We introduce the recursive divisor function, a recursive analog of the usual divisor function. This is bounded in terms of values of the Riemann zeta function. We give a geometric interpretation of recursive divisibility, and study the number and sum of recursive divisors. By computing those numbers that are more recursively divisible than all of their predecessors, we recover many of the numbers prevalent in design.