Question 1
Let $l(n)$ denote the greatest odd divisor of any natural number $n$. Find the sum
$$
l(1) + l(2) + l(3) + \cdots + l(2^{2013}). \qquad (\text{Michal Rol\'inek})
$$
$$
l(1) + l(2) + l(3) + \cdots + l(2^{2013}). \qquad (\text{Michal Rol\'inek})
$$