Given a range [L, R], the task is to find the numbers from the range which have the count of their divisors as even as well as prime.
Then, print the count of the numbers found. The values of L and R are less than 10^6 and L< R.
Input: L=3, R=9 Output: Count = 3 Explanation: The numbers are 3, 5, 7 Input : L=3, R=17 Output : Count: 6
- The only number that is prime, as well as even, is ‘2’.
- So, we need to find all the numbers within the given range that have exactly 2 divisors,
i.e. prime numbers.
A simple approach:
- Start a loop from ‘l’ to ‘r’ and check whether the number is prime(it will take more time for bigger range).
- If the number is prime then increment the count variable.
- At the end, print the value of count.
An efficient approach:
- We have to count the prime numbers in range [L, R].
- First, create a sieve which will help in determining whether the number is prime or not in O(1) time.
- Then, create a prefix array to store the count of prime numbers where, element at index ‘i’ holds the count of the prime numbers from ‘1’ to ‘i’.
- Now, if we want to find the count of prime numbers in range [L, R], the count will be (sum[R] – sum[L-1])
- Finally, print the result i.e. (sum[R] – sum[L-1])
Below is the implementation of the above approach:
- Sum of all prime divisors of all the numbers in range L-R
- Count of numbers below N whose sum of prime divisors is K
- Program to find count of numbers having odd number of divisors in given range
- Count numbers from range whose prime factors are only 2 and 3
- Queries for the difference between the count of composite and prime numbers in a given range
- Count numbers in a range having GCD of powers of prime factors equal to 1
- Count Numbers in Range with difference between Sum of digits at even and odd positions as Prime
- Count total divisors of A or B in a given range
- Count occurrences of a prime number in the prime factorization of every element from the given range
- Find numbers with n-divisors in a given range
- Find numbers with K odd divisors in a given range
- Find the number of divisors of all numbers in the range [1, n]
- Count elements in the given range which have maximum number of divisors
- Count the numbers < N which have equal number of divisors as K
- Sum of all the prime numbers in a given range
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