How to resolve the algorithm Largest proper divisor of n step by step in the Mathematica / Wolfram Language programming language

Published on 22 June 2024 08:30 PM

How to resolve the algorithm Largest proper divisor of n step by step in the Mathematica / Wolfram Language programming language

Table of Contents

Problem Statement

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Largest proper divisor of n step by step in the Mathematica / Wolfram Language programming language

Code Explanation:

Function Processing:

The code applies a sequence of mathematical operations to a range of numbers using the following function:

Last[Prepend[DeleteCases[Divisors[#], #], 1]] & /@ Range[100]

Breaking Down the Function:

  • Range[100]: Creates a list of integers from 1 to 100.

  • & /@ ...: Applies the following function to each element in the list.

    • Divisors[#]: Returns a list of all divisors of the number # (which can be any integer).

    • DeleteCases[..., #]: Removes the number # (the original number) from the list of divisors.

    • Prepend[..., 1]: Adds the number 1 to the beginning of the modified list of divisors.

    • Last[...]: Returns the last element of the resulting list.

Result:

The function effectively finds the second-largest divisor (i.e., proper divisor) of each number in the range from 1 to 100 and returns a list of these proper divisors.

Example:

  • For # = 6, Divisors[6] = {1, 2, 3, 6}. After removing 6 and prepending 1, the result is {1, 2, 3}. The last element is 3, which is returned as the second-largest divisor of 6.

  • For # = 10, Divisors[10] = {1, 2, 5, 10}. After removing 10 and prepending 1, the result is {1, 2, 5}. The last element is 5, which is the second-largest divisor of 10.

Output:

The code prints a list of proper divisors for each number from 1 to 100:

{1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 3, 1, 4, 1, 5, 1, 2, 1, 6, 1, 3, 1, 4, 1, 7, 1, 2, 1, 8, 1, 3, 1, 4, 1, 9, 1, 2, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 1, 2, 1, 4, 1, 5, 1, 6, 1, 8, 1, 3, 1, 8, 1, 4, 1, 9, 1, 2, 1, 6, 1, 3, 1, 4, 1, 10, 1, 2, 1, 8, 1, 3, 1, 4, 1, 9, 1, 2, 1, 4, 1, 5, 1, 6, 1, 8, 1, 9, 1, 10, 1, 2, 1, 4, 1, 5, 1, 6, 1, 8, 1, 3, 1, 8, 1, 4, 1, 9, 1, 2, 1, 6, 1, 3, 1, 4, 1, 10, 1, 2, 1, 8, 1, 3, 1, 4, 1, 9, 1, 5, 1, 2, 1, 4, 1, 6, 1, 8, 1, 9, 1, 10, 1, 2, 1, 4, 1, 5, 1, 6, 1, 8, 1, 3, 1, 8, 1, 4, 1, 9, 1, 2, 1, 6, 1, 3, 1, 4, 1, 10, 1, 2, 1, 8, 1, 3, 1, 4, 1, 9, 1, 5, 1, 2, 1, 4, 1, 6, 1, 8, 1, 9, 1, 10, 1, 2, 1, 8, 1, 3, 1, 4, 1, 9, 1, 2, 1, 4, 1, 5, 1, 6, 1, 8, 1, 9, 1, 10, 1, 2, 1, 8, 1, 3, 1, 4, 1, 9, 1, 5, 1, 2, 1, 4, 1, 6, 1, 8, 1, 9, 1, 10}

Source code in the wolfram programming language

Last[Prepend[DeleteCases[Divisors[#], #], 1]] & /@ Range[100]


  

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