Step by Step solution about How to resolve the algorithm Arithmetic derivative step by step in the Julia programming language

The provided Julia code calculates and displays the D(n) function for a range of integers and also computes D for powers of 10 divided by 7. Here's a breakdown:

1. using Primes: This line imports the Primes package, which provides functions for working with prime numbers.

2. D(n) = ...: This is a function definition that calculates the D(n) function for a given integer n. It has the following behavior:

   • If n is negative, it returns the negation of D(-n).
   • If n is less than 2, it returns zero.
   • If n is prime, it returns one.
   • Otherwise, it computes the sum of (e * n ÷ p) for each prime factor (p, e) of n, where p is a prime factor and e is its exponent.

3. foreach(p -> print(lpad(p[2], 5), p[1] % 10 == 0 ? "\n" : ""), pairs(map(D, -99:100))): This code uses the foreach macro to iterate over pairs of values from the pairs of the result of map(D, -99:100). It prints the second element (p[2]) of each pair, left-padded with spaces to a width of 5. If the first element (p[1]) is a multiple of 10, it prints a newline after each value to keep the output aligned. This effectively prints D(n) for n from -99 to 100.

4. println(): This prints a newline to separate the previous output from the following.

5. for m in 1:20: This starts a loop that iterates over m from 1 to 20.

6. println("D for 10^", rpad(m, 3), "divided by 7 is ", D(Int128(10)^m) ÷ 7): Within the loop, for each value of m, it prints a string stating "D for 10^m divided by 7 is" and the result of dividing D(10^m) by 7. The rpad function is used to right-pad the string representation of m with spaces to a width of 3 for better alignment.

using Primes

D(n) = n < 0 ? -D(-n) : n < 2 ? zero(n) : isprime(n) ? one(n) : typeof(n)(sum(e * n ÷ p for (p, e) in eachfactor(n)))

foreach(p -> print(lpad(p[2], 5), p[1] % 10 == 0 ? "\n" : ""), pairs(map(D, -99:100)))

println()
for m in 1:20
    println("D for 10^", rpad(m, 3), "divided by 7 is ", D(Int128(10)^m) ÷ 7)
end