# Problem 484: Arithmetic Derivative

![graphic](img484.gif)

The arithmetic derivative is defined by p' = 1 for any prime p (ab)' =
a'b + ab' for all integers a, b (Leibniz rule) For example, 20' = 24
Find ∑ gcd(k,k') for 1 < k ≤ 5·1015 Note: gcd(x,y) denotes the
greatest common divisor of x and y.