Arithmetic Derivative (noch nicht übersetzt)

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.