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Given an integer N, consider the set {floor(N/1), floor(N/2), floor(N/3), …, floor(N/N)}, where floor(x) is the greatest integer less than or equal to x. You need to find the number of distinct integers in this set. For example, suppose N is 5. Then, the set is {floor(5/1), floor(5/2), floor(5/3), floor(5/4), floor(5/5)}={floor(5), floor(2.5), floor(1.666…), floor(1.25), floor(1)} = {5,2,1,1,1}. There are 3 distinct elements in this set (1,2,5), and so the answer for this would be 3. Find the number of distinct integers in the set {floor(N/1),…,floor(N/N)} for the following values of N:
(a) N = 38 (b) N = 146 © N = 2808

last question of zonal informatics olympaid 2020