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Find sum of odd factors of a number

  • Difficulty Level : Medium
  • Last Updated : 23 Mar, 2021

Given a number n, the task is to find the odd factor sum.
Examples : 
 

Input : n = 30
Output : 24
Odd dividers sum 1 + 3 + 5 + 15 = 24 

Input : 18
Output : 13
Odd dividers sum 1 + 3 + 9 = 13

 

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Prerequisite : Sum of all the factors of a number
As discussed in above mentioned previous post, sum of factors of a number is 
Let p1, p2, … pk be prime factors of n. Let a1, a2, .. ak be highest powers of p1, p2, .. pk respectively that divide n, i.e., we can write n as n = (p1a1)*(p2a2)* … (pkak)
 

Sum of divisors = (1 + p1 + p12 ... p1a1) * 
                  (1 + p2 + p22 ... p2a2) *
                  .............................................
                  (1 + pk + pk2 ... pkak) 

To find sum of odd factors, we simply need to ignore even factors and their powers. For example, consider n = 18. It can be written as 2132 and sun of all factors is (1)*(1 + 2)*(1 + 3 + 32). Sum of odd factors (1)*(1+3+32) = 13.
To remove all even factors, we repeatedly divide n while it is divisible by 2. After this step, we only get odd factors. Note that 2 is the only even prime.
 

C++




// Formula based CPP program
// to find sum of all
// divisors of n.
#include <bits/stdc++.h>
using namespace std;
 
// Returns sum of all factors of n.
int sumofoddFactors(int n)
{
    // Traversing through all
    // prime factors.
    int res = 1;
 
    // ignore even factors by
    // removing all powers of
    // 2
    while (n % 2 == 0)
        n = n / 2;
 
    for (int i = 3; i <= sqrt(n); i++)
    {
 
        // While i divides n, print
        // i and divide n
        int count = 0, curr_sum = 1;
        int curr_term = 1;
        while (n % i == 0) {
            count++;
 
            n = n / i;
 
            curr_term *= i;
            curr_sum += curr_term;
        }
 
        res *= curr_sum;
    }
 
    // This condition is to handle
    // the case when n is a prime
    // number.
    if (n >= 2)
        res *= (1 + n);
 
    return res;
}
 
// Driver code
int main()
{
    int n = 30;
    cout << sumofoddFactors(n);
    return 0;
}

Java




// Formula based Java program
// to find sum of all divisors
// of n.
import java.io.*;
import java.math.*;
 
class GFG {
     
    // Returns sum of all
    // factors of n.
    static int sumofoddFactors(int n)
    {
        // Traversing through
        // all prime factors.
        int res = 1;
     
        // ignore even factors by
        // removing all powers
        // of 2
        while (n % 2 == 0)
            n = n / 2;
     
        for (int i = 3; i <= Math.sqrt(n); i++)
        {
     
            // While i divides n, print i
            // and divide n
            int count = 0, curr_sum = 1;
            int curr_term = 1;
            while (n % i == 0)
            {
                count++;
     
                n = n / i;
     
                curr_term *= i;
                curr_sum += curr_term;
            }
     
            res *= curr_sum;
             
        }
     
        // This condition is to handle
        // the case when n is a
        // prime number.
        if (n >= 2)
            res *= (1 + n);
     
        return res;
    }
     
    // Driver code
    public static void main(String args[])
                        throws IOException
    {
        int n = 30;
        System.out.println(sumofoddFactors(n));
    }
}
 
/* This code is contributed by Nikita Tiwari.*/

Python3




# Formula based Python3 program
# to find sum of all divisors
# of n.
import math
 
# Returns sum of all factors
# of n.
def sumofoddFactors( n ):
     
    # Traversing through all
    # prime factors.
    res = 1
     
    # ignore even factors by
    # of 2
    while n % 2 == 0:
        n = n // 2
     
    for i in range(3, int(math.sqrt(n) + 1)):
         
        # While i divides n, print
        # i and divide n
        count = 0
        curr_sum = 1
        curr_term = 1
        while n % i == 0:
            count+=1
             
            n = n // i
            curr_term *= i
            curr_sum += curr_term
         
        res *= curr_sum
     
    # This condition is to
    # handle the case when
    # n is a prime number.
    if n >= 2:
        res *= (1 + n)
     
    return res
 
# Driver code
n = 30
print(sumofoddFactors(n))
 
# This code is contributed by "Sharad_Bhardwaj".

C#




// Formula based C# program to
// find sum of all divisors of n.
using System;
 
class GFG {
     
    // Returns sum of all
    // factors of n.
    static int sumofoddFactors(int n)
    {
        // Traversing through
        // all prime factors.
        int res = 1;
     
        // ignore even factors by
        // removing all powers
        // of 2
        while (n % 2 == 0)
            n = n / 2;
     
        for (int i = 3; i <= Math.Sqrt(n); i++)
        {
            // While i divides n, print i
            // and divide n
            int count = 0, curr_sum = 1;
            int curr_term = 1;
            while (n % i == 0)
            {
                count++;
                n = n / i;
     
                curr_term *= i;
                curr_sum += curr_term;
            }
     
            res *= curr_sum;
        }
     
        // This condition is to handle
        // the case when n is a
        // prime number.
        if (n >= 2)
            res *= (1 + n);
     
        return res;
    }
     
    // Driver code
    public static void Main(String[] argc)
    {
        int n = 30;
        Console.Write(sumofoddFactors(n));
    }
}
 
/* This code is contributed by parashar...*/

PHP




<?php
// Formula based PHP program
// to find sum of all
// divisors of n.
 
// Returns sum of all factors of n.
function sumofoddFactors($n)
{
    // Traversing through all
    // prime factors.
    $res = 1;
 
    // ignore even factors by
    // removing all powers of
    // 2
    while ($n % 2 == 0)
        $n = $n / 2;
 
    for ($i = 3; $i <= sqrt($n); $i++)
    {
 
        // While i divides n, print
        // i and divide n
        $count = 0; $curr_sum = 1;
        $curr_term = 1;
        while ($n % $i == 0)
        {
            $count++;
 
            $n = $n / $i;
 
            $curr_term *= $i;
            $curr_sum += $curr_term;
        }
 
        $res *= $curr_sum;
    }
 
    // This condition is to
    // handle the case when
    // n is a prime number.
    if ($n >= 2)
        $res *= (1 + $n);
 
    return $res;
}
 
// Driver code
$n = 30;
echo sumofoddFactors($n);
 
// This code is contributed
// by nitin mittal.
?>

Javascript




<script>
 
// Formula based Javascript program
// to find sum of all
// divisors of n.
 
// Returns sum of all factors of n.
function sumofoddFactors(n)
{
    // Traversing through all
    // prime factors.
    let res = 1;
 
    // ignore even factors by
    // removing all powers of
    // 2
    while (n % 2 == 0)
        n = n / 2;
 
    for (let i = 3; i <= Math.sqrt(n); i++)
    {
 
        // While i divides n, print
        // i and divide n
        let count = 0;
        let curr_sum = 1;
        let curr_term = 1;
        while (n % i == 0)
        {
            count++;
 
            n = n / i;
 
            curr_term *= i;
            curr_sum += curr_term;
        }
 
        res *= curr_sum;
    }
 
    // This condition is to
    // handle the case when
    // n is a prime number.
    if (n >= 2)
        res *= (1 + n);
 
    return res;
}
 
// Driver code
let n = 30;
document.write(sumofoddFactors(n));
 
// This code is contributed by _saurabh_jaiswal
 
</script>

Output : 

24

 




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