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.