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Arithmetic Derivative

Published on Saturday, 11th October 2014, 01:00 pm; Solved by 211;
Difficulty rating: 100%

Problem 484

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.