n = n n' = n

Number Theory Level pending

What is the sum of the first two positive integers which satisfy n = n n' = n , where n n' is the arithmetic derivative of n n ?

Clarification: The arithmetic derivative of n n is given by:

  • n = 0 n' = 0 for n n = 1 or 0.
  • n = 1 n' = 1 if is prime.
  • n = a b + b a n' = a'b + b'a if n n is composite, where a a and b b are factors of n n


The answer is 31.

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1 solution

Geoff Pilling
Apr 12, 2016

The first two such numbers are 4 and 27. And 4+27 = 31

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