# Arithmetic derivative

Author: mathforces
Problem has been solved: 42 times

Русский язык | English Language

Find the sum of all natural numbers $n <1000$ such that $D (n) = n$ if $D(n)$ is the arithmetic derivative which is defined as follows:
• $D (1) = 0$,
• $D (p) = 1$ for all primes $p$,
• $D (ab) = D (a) b + D (b) a$, for all natural numbers $a$ and $b$.