In this article, we study an optimized way to calculate the distinct prime factorization up to n natural number using O O(n*log n) time complexity with pre-computation allowed.
Key Concept: Our idea is to store the Smallest Prime Factor(SPF) for every number. Then to calculate the distinct prime factorization of the given number by dividing the given number recursively with its smallest prime factor till it becomes 1.
To calculate to smallest prime factor for every number we will use the sieve of eratosthenes. In original Sieve, every time we mark a number as not-prime, we store the corresponding smallest prime factor for that number (Refer this article for better understanding).
The implementation for the above method is given below :
- Print all numbers whose set of prime factors is a subset of the set of the prime factors of X
- Maximum number of prime factors a number can have with exactly x factors
- Check if a number exists having exactly N factors and K prime factors
- Number which has the maximum number of distinct prime factors in the range M to N
- Distinct Prime Factors of Array Product
- Distinct Prime Factors of an Array
- Find number of factors of N when location of its two factors whose product is N is given
- Print numbers such that no two consecutive numbers are co-prime and every three consecutive numbers are co-prime
- Number of factors of very large number N modulo M where M is any prime number
- First element of every K sets having consecutive elements with exactly K prime factors less than N
- Find all Factors of Large Perfect Square Natural Number in O(sqrt(sqrt(N))
- Permutation of first N positive integers such that prime numbers are at prime indices
- Permutation of first N positive integers such that prime numbers are at prime indices | Set 2
- First N natural can be divided into two sets with given difference and co-prime sums
- Numbers less than N which are product of exactly two distinct prime numbers
- Super Ugly Number (Number whose prime factors are in given set)
- Number with maximum number of prime factors
- K-Primes (Numbers with k prime factors) in a range
- Count numbers from range whose prime factors are only 2 and 3
- Common prime factors of two numbers
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