D(0) = D(1) = 0

D(prime) = 1

D(ab) = D(a)*b + D(b)*a

Examples:

D(7) = 1 because 7 is prime.

D(30) = D(5*6) = D(5)*6 + 5*D(6) = 1*6 + 5*D(2*3)

= 6 + 5*[D(2)*3+2*D(3)] = 6 + 5*5 = 31, so ...

D(30) = 31

D(58) = 31 (More than one integer can have the same Arithmetic Derivative.)

(1). Find n and D(n) (n up to 5 digits) such that D(n) is the largest.

(2). Find n and D(n) (n up to 5 digits and **not prime**) such that the ratio D(n)/n is the largest.

(3). Which 4-digit Palindrome is the Arithmetic Derivative of the **most** 4-digit positive integers, and list them.

(4). For what set of n is n = D(n)