Pseudo Primes Complete Solution

This article is part of the Scaler Topics Fortnightly Contest - 18

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Solution Approach

The naive approach will be to iterate over all the numbers.
Find their prime factors sum them and check if the sum is prime.
But this is too slow as iterating over the range is O(N) and then prime factorisation is O(sqrt(N)) and then checking
if the sum is prime is another O(sqrt(N)).
Overall time complexity is O(N sqrt(N)) which is slow for the given constraints.
Try to use Sieve of Eratosthenis.
We use Sieve. Since we only need to sum the distinct prime factors whenever we find a prime number i using sieve
we iterate over its multiples and add i to its sum. Keep another prefix array for pseudo primes update it while running sieve.

Time Complexity - O(N log log(N)) Space Complexity - O(N)