There are Q queries. Each query is of the form of L and R. The task is to output sum of number of prime factors of each number in the given range of each query.
Input : Q = 2 L = 6, R = 10 L = 1, R = 5 Output : 7 4 For query 1, 6 => 2 [Prime factors are 2 and 3] 7 => 1 8 => 1 9 => 1 10 => 2 Sum = 2 + 1 + 1 + 1 + 2 = 7 For query 2, 1 => 0 2 => 1 3 => 1 4 => 1 5 => 1 Sum = 0 + 1 + 1 + 1 + 1 = 4.
Method 1 (brute force):
The idea is to traverse from L to R for each query, and for each number find the number of prime factor and add to the answer.
Method 2 (efficient approach):
The idea is to use the Sieve of Eratosthenes method for counting the number of prime factor of composite numbers. Just like, the inner loop of Sieve of Eratosthenes is used to mark composite number. We can use it for incrementing the prime factor of numbers. Instead of marking each array cell as 0 or 1, we can store the number of prime number of that index. And then for each query, find the sum of array from L to R.
Below is the implementation of this approach:
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- Queries to count integers in a range [L, R] such that their digit sum is prime and divisible by K
- Queries for the difference between the count of composite and prime numbers in a given range
- Queries for counts of multiples in an array
- Prime Factor
- k-th prime factor of a given number
- N-th prime factor of a given number
- Least prime factor of numbers till n
- Exactly n distinct prime factor numbers from a to b
- Count all the numbers less than 10^6 whose minimum prime factor is N
- Nearest element with at-least one common prime factor
- Find largest prime factor of a number
- Sum of largest prime factor of each number less than equal to n
- Find sum of a number and its maximum prime factor
- Most frequent factor in a range of integers
- Count of subarrays whose products don't have any repeating prime factor