Problem 47843. Compute the arithmetic derivative of integers

The Lagarias arithmetic derivative D(n) is defined for integers such that the derivative of a prime number is 1: D(p) = 1. It also satisfies the Leibniz formula, which resembles the product rule of calculus:
D(mn) = mD(n)+nD(m)
For example, the arithmetic derivative of 15 is 3D(5) + 5D(3) = 3x1 + 5x1 = 8. The Leibniz formula also implies that D(1) = 0.
Write a function to compute the arithmetic derivative of a natural number.
Solve

Solution Stats

42.25% Correct | 57.75% Incorrect
Last Solution submitted on Nov 29, 2025

Solution Comments

Show comments

Problem Recent Solvers26

Suggested Problems

More from this Author315

Community Treasure Hunt

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

Start Hunting!