Cody Problem 47843 involved the arithmetic derivative of integers. In particular, D(p) = 1 if p is prime and D(mn) = n D(m) + m D(n). Therefore, the arithmetic derivatives of 1, 2, 3, 4, 5, and 6 are 0, 1, 1, 4, 1, and 5, respectively.
One might then ask about solving arithmetic differential equations (ADEs). Because the study of differential equations often starts with solving dy/dx = y, let’s consider the analogous ADE D(n) = n. The definition of the arithmetic derivative shows that no prime can solve this equation, but the sample calculations above show that the first (i.e., m = 1) solution is 4.
Write a function to compute the mth solution to this ADE. Because the solutions become large quickly, return the logarithm of the solution.
Solve

Solution Stats

38 Solutions

13 Solvers

Last Solution submitted on May 25, 2026

Last 200 Solutions

Solution Comments

Show comments

Problem Recent Solvers13

Chris Cleveland George Berken Christian Schröder Mehdi Dehghan

Suggested Problems

More from this Author323

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!