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 Arithmetic Derivative (Posted on 2022-06-10)
Consider the following (simplified) definition of the "Arithmetic Derivative" for n in positive integers:
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)

 No Solution Yet Submitted by Larry Rating: 5.0000 (1 votes)

 Subject Author Date re: bits and pieces Charlie 2022-06-10 15:50:51 bits and pieces Larry 2022-06-10 15:05:44 Python version for 1 & 2 Charlie 2022-06-10 14:47:36 re(2): part (3) expanded to 5-digit n (continued) Charlie 2022-06-10 11:10:09 re: part (3) expanded to 5-digit n (continued) Charlie 2022-06-10 11:09:09 part (3) expanded to 5-digit n Charlie 2022-06-10 11:07:23 computer solution Charlie 2022-06-10 11:02:48

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