a) define f(k) as the largest power of 2 that divides k. For example, f(25) = 1, f(42) = 2, f(144) = 16. What is ${1 \over k}\sum_1^k f(k)$?
b) define f(k) as the square of largest power of 2 that divides k. For example, f(25) = 1, f(42) = 4, f(144) = 256 What is ${1 \over k}\sum_1^k f(k)$?
c) define f(k) as the number of divisors of k. For example, f(25) = 3 (1,5,25), f(42) = 9 (1,2,3,6,7,12,14,21,42) What is ${1 \over k}\sum_1^k f(k)$?