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Arithmetic Derivative

Problem 484

Published on 11 October 2014 at 01:00 pm [Server Time]

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.


Answer not yet available
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