Modify the Eratosthenes Sieve to count the number of all divisors of the given number. Find an algorithm which for given number N <= 10000 will create a field of N numbers such that the value of the i-th element of the field is the number of all divisors of the number i for each i <= N, but the solution mustn´t be worse than O(n.log n). I don´t have any idea how to proceed if I should satisfy the given maximal difficulty. Can anybody give me some hint? Thank you.