How to resolve the algorithm Tau function step by step in the AppleScript programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Tau function step by step in the AppleScript programming language

Table of Contents

Problem Statement

Given a positive integer, count the number of its positive divisors.

Show the result for the first   100   positive integers.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Tau function step by step in the AppleScript programming language

Source code in the applescript programming language

on factorCount(n)
    if (n < 1) then return 0
    set counter to 2
    set sqrt to n ^ 0.5
    if (sqrt mod 1 = 0) then set counter to 1
    repeat with i from (sqrt div 1) to 2 by -1
        if (n mod i = 0) then set counter to counter + 2
    end repeat
    
    return counter
end factorCount

-- Task code:
local output, n, astid
set output to {"Positive divisor counts for integers 1 to 100:"}
repeat with n from 1 to 100
    if (n mod 20 = 1) then set end of output to linefeed
    set end of output to text -3 thru -1 of ("  " & factorCount(n))
end repeat
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to ""
set output to output as text
set AppleScript's text item delimiters to astid
return output


"Positive divisor counts for integers 1 to 100:
  1  2  2  3  2  4  2  4  3  4  2  6  2  4  4  5  2  6  2  6
  4  4  2  8  3  4  4  6  2  8  2  6  4  4  4  9  2  4  4  8
  2  8  2  6  6  4  2 10  3  6  4  6  2  8  4  8  4  4  2 12
  2  4  6  7  4  8  2  6  4  8  2 12  2  4  6  6  4  8  2 10
  5  4  2 12  4  4  4  8  2 12  4  6  4  4  4 12  2  6  6  9"


  

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