Comments on the OEIS sequence D(n) are insteresting: https://oeis.org/A003415 https://oeis.org/A003415. One in particular points out that if we take the prime f

Comments on the OEIS sequence D(n) are insteresting: https://oeis.org/A003415 https://oeis.org/A003415. One in particular points out that if we take the prime factorization of n = p0*p1*...*pk, where the pi aren't necessarily distinct, then over the reals lim (p0+h)(p1+h)...(pk+h) - p0*p1*...*pk D(n) = h->0 ------------------------------------ . h This motivates the D(p)=1 definition, meaning we can take D to be defined just by the Leibniz rule. (Note that D(1) = D(1*1) = 1*D(1) + D(1)*1 = 2*D(1), implying that D(1)=0, so that part of the definition is redundant.) Others have pointed out that the definition also works for any unique factorization domain, and in the case of polynomials, the Leibniz rule guarantees D agrees with the standard derivative, which is also a nice sanity check.