How to resolve the algorithm Largest proper divisor of n step by step in the Mathematica / Wolfram Language programming language
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 removing6
and prepending1
, the result is{1, 2, 3}
. The last element is3
, which is returned as the second-largest divisor of6
. -
For
# = 10
,Divisors[10]
={1, 2, 5, 10}
. After removing10
and prepending1
, the result is{1, 2, 5}
. The last element is5
, which is the second-largest divisor of10
.
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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