Question 2
A positive integer is fancy if it is a sum
$$2^{a_1}+2^{a_2}+\cdots+2^{a_{100}},$$
where the exponents are nonnegative integers, not necessarily distinct. Find the smallest positive integer $n$ such that no multiple of $n$ is fancy.
$$2^{a_1}+2^{a_2}+\cdots+2^{a_{100}},$$
where the exponents are nonnegative integers, not necessarily distinct. Find the smallest positive integer $n$ such that no multiple of $n$ is fancy.