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!
- Python Program for Number of elements with odd factors in given range
- Python Program for Find sum of even factors of a number
- Python Program for Find minimum sum of factors of number
- Python Program for Efficient program to print all prime factors of a given number
- Python Program for Product of unique prime factors of a number
- Python Program to Find the Number Occurring Odd Number of Times
- Python program to find the sum of all even and odd digits of an integer list
- Python Program to find Sum of Negative, Positive Even and Positive Odd numbers in a List
- Python - Factors Frequency Dictionary
- Python - Elements with factors count less than K
- Python Program to create an OTP by squaring and concatenating the odd digits of a number
- Python Program to Print Largest Even and Largest Odd Number in a List
- Python Program to Determine Whether a Given Number is Even or Odd Recursively
- Python Program for Program to find the sum of a Series 1/1! + 2/2! + 3/3! + 4/4! +.......+ n/n!
- Python Program for Odd-Even Sort / Brick Sort
- Python Program for Check if count of divisors is even or odd
- Python Program for Difference between sums of odd and even digits
- Python program to copy odd lines of one file to other
- Python program to count Even and Odd numbers in a List
- Python program to print all odd numbers in a range