Given a number n, the task is to find the even factor sum of a number.
Input : 30 Output : 48 Even dividers sum 2 + 6 + 10 + 30 = 48 Input : 18 Output : 26 Even dividers sum 2 + 6 + 18 = 26
Prerequisite : Sum of factors
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)
If number is odd, then there are no even factors, so we simply return 0.
If number is even, we use above formula. We only need to ignore 20. All other terms multiply to produce even factor sum. For example, consider n = 18. It can be written as 2132 and sun of all factors is (20 + 21)*(30 + 31 + 32). if we remove 20 then we get the
Sum of even factors (2)*(1+3+32) = 26.
To remove odd number in even factor, we ignore then 20 whaich is 1. After this step, we only get even factors. Note that 2 is the only even prime.
Below is the implementation of the above approach.
- Find number of factors of N when location of its two factors whose product is N is given
- Find sum of odd 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
- Super Ugly Number (Number whose prime factors are in given set)
- Queries on sum of odd number digit sums of all the factors of a number
- 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
- Prime factors of a big number
- Product of factors of number
- Maximize the product of four factors of a Number
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Improved By : Mithun Kumar