Given a range [n, m], the task is to find the number of elements that have even number of factors in the given range (n and m inclusive).
Input: n = 5, m = 20 Output: 14 The numbers with even factors are 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20. Input: n = 5, m = 100 Output: 88
A Simple Solution is to loop through all numbers starting from n. For every number, check if it has an even number of factors. If it has an even number of factors then increment count of such numbers and finally print the number of such elements. To find all divisors of a natural number efficiently, refer All divisors of a natural number
An Efficient Solution is to find the numbers with odd number of factors i.e only the perfect squares have odd number of factors, so all numbers other than perfect squares will have even number of factors. So, find the count of perfect squares in the range and subtract from the total numbers i.e. m-n+1 .
Below is the implementation of the above approach:
Count is 88
- Number of elements with odd factors in given range
- Sum of all odd factors of numbers in the range [l, r]
- Sum of all even factors of numbers in the range [l, r]
- Count numbers from range whose prime factors are only 2 and 3
- K-Primes (Numbers with k prime factors) in a range
- Count elements in the given range which have maximum number of divisors
- Count numbers in a range having GCD of powers of prime factors equal to 1
- Prime factors of LCM of array elements
- Minimum elements to be added in a range so that count of elements is divisible by K
- 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 sum of odd factors of a number
- Find sum of even factors of a number
- Product of factors of number
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