I am surprised that Mathworld Wolfram did not list "Arithmetic Derivative" but Wiki has

http://en.wikipedia.org/wiki/Arithmetic_derivative

You can use Arithmetic Derivative to formulate Goldbach's conjecture, twin prime and prime triples in an alternative way.

E. J. Barbeau, "Remark on an arithmetic derivative", Canad. Math. Bull. 4 (1961), 117 http://www.maa.org/mathland/mathtrek_03_22_04.html

Ufnarovski and Åhlander (2003) http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Ufnarovski/ufnarovski.pdf

Why didn't Weisstein's Mathworld mention arithmetic derivative at all?

@Benvitale