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
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.
- Find number of factors of N when location of its two factors whose product is N is given
- Find sum of even factors of a number
- Find minimum sum of factors of number
- Queries to find whether a number has exactly four distinct factors or not
- Number which has the maximum number of distinct prime factors in the range M to N
- Queries on sum of odd number digit sums of all the factors of a number
- Super Ugly Number (Number whose prime factors are in given set)
- Number with maximum number of prime factors
- Sum of all the factors of a number
- Find four factors of N with maximum product and sum equal to N | Set 3
- Find four factors of N with maximum product and sum equal to N
- Find four factors of N with maximum product and sum equal to N | Set-2
- Product of factors of number
- Prime factors of a big number
- Sort on the basis of number of factors using STL
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.