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Arithmetic derivative

Author: mathforces
Problem has been solved: 39 times

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Find the sum of all natural numbers $ n <1000 $ such that $ D (n) = n $ if $D(n)$ is the arithmetic derivative which is defined as follows:
  • $ D (1) = 0 $,
  • $ D (p) = 1 $ for all primes $ p $,
  • $ D (ab) = D (a) b + D (b) a $, for all natural numbers $ a $ and $ b $.





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