For every positive integer k let a(k) be the largest integer such that 2a(k) divides k. For every positive integer n determine a(1)+a(2)+⋯+a(2n).
Source: Pan African MO 2006 Q4
Tags: floor function, number theory unsolved, number theory
For every positive integer k let a(k) be the largest integer such that 2a(k) divides k. For every positive integer n determine a(1)+a(2)+⋯+a(2n).