Given a number n, the task is to find the odd factor sum.
Input : n = 30 Output : 24 Odd dividers sum 1 + 3 + 5 + 15 = 24 Input : 18 Output : 13 Odd dividers sum 1 + 3 + 9 = 13
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.
Please refer complete article on Find sum of odd factors of a number for more details!
- Java Program for Number of elements with odd factors in given range
- Java Program to Find sum of even factors of a number
- Java Program to Find minimum sum of factors of number
- Java Program to find Product of unique prime factors of a number
- Java Program for efficiently print all prime factors of a given number
- Java Program to Find the Number Occurring Odd Number of Times
- Java Program to Find the Sum of First N Odd & Even Numbers
- Java Program to Find Maximum Odd Number in Array Using Stream and Filter
- Java Program to Find the Frequency of Odd & Even Numbers in the Matrix
- Java Program for Odd-Even Sort / Brick Sort
- Java Program to Check if count of divisors is even or odd
- Java Program for Difference between sums of odd and even digits
- Java Program to Check if a Given Integer is Odd or Even
- Java Program to Store Even & Odd Elements of an Array into Separate Arrays
- Java Program to Print the Elements of an Array Present on Odd Position
- Java Program to Reverse a Number and find the Sum of its Digits Using do-while Loop
- Java Program for Program to find area of a circle
- Java Program to find the sum of a Series 1/1! + 2/2! + 3/3! + 4/4! +.......+ n/n!
- Java Program to find sum of array
- Java Program to Find sum of Series with n-th term as n^2 - (n-1)^2