Step by Step solution about How to resolve the algorithm Proper divisors step by step in the Go programming language

Explanation:

This Go program is designed to find and count the proper divisors of numbers up to a specified limit. Here's a detailed breakdown:

1. listProperDivisors Function:

• It takes an integer limit as input.
• Iterates through numbers from 1 to limit.
• For each number i, it prints i and its proper divisors. Proper divisors are divisors of i that are less than i.
• If i is 1 (not a proper divisor), it indicates that it has no proper divisors.

2. countProperDivisors Function:

• It takes an integer n as input.
• Counts the number of proper divisors of n and returns the count.
• It iterates through numbers from 1 to half of n (inclusive), checking if each one divides evenly into n.

3. main Function:

• Finding Proper Divisors:

  • Calls the listProperDivisors function with a limit of 10 to print the proper divisors of numbers up to 10.

• Finding Numbers with the Most Proper Divisors:

  • Initializes variables to keep track of the maximum number of proper divisors (maxCount) and the numbers with the maximum proper divisors (most).
  • Iterates through numbers from 2 to 20,000.
  • For each number n, it uses the countProperDivisors function to count its proper divisors.
  • If the count matches the current maximum, it adds n to the list of numbers with the maximum count.
  • If the count is greater than the maximum, it updates the maximum count and replaces the list of numbers with a single entry for n.

• Printing the Results:

  • Prints the numbers with the maximum number of proper divisors and the maximum count.
  • Iterates through and prints each number in the most list, which contains the numbers with the maximum proper divisors.

package main

import (
    "fmt"
    "strconv"
)

func listProperDivisors(limit int) {
    if limit < 1 {
        return
    }
    width := len(strconv.Itoa(limit))
    for i := 1; i <= limit; i++ {
        fmt.Printf("%*d -> ", width, i)
        if i == 1 {
            fmt.Println("(None)")
            continue
        }
        for j := 1; j <= i/2; j++ {
            if i%j == 0 {
                fmt.Printf(" %d", j)
            }
        }
        fmt.Println()
    }
}

func countProperDivisors(n int) int {
    if n < 2 {
        return 0
    }
    count := 0
    for i := 1; i <= n/2; i++ {
        if n%i == 0 {
            count++
        }
    }
    return count
}

func main() {
    fmt.Println("The proper divisors of the following numbers are :\n")
    listProperDivisors(10)
    fmt.Println()
    maxCount := 0
    most := []int{1}
    for n := 2; n <= 20000; n++ {
        count := countProperDivisors(n)
        if count == maxCount {
            most = append(most, n)
        } else if count > maxCount {
            maxCount = count
            most = most[0:1]
            most[0] = n
        }
    }
    fmt.Print("The following number(s) <= 20000 have the most proper divisors, ")
    fmt.Println("namely", maxCount, "\b\n")
    for _, n := range most {
        fmt.Println(n)
    }
}