Two positive integers $n,m\ge 2$ are called allies if when written as a product of primes (not necessarily different): $n=p_1p_2...p_s$ and $m=q_1q_2...q_t$, turns out that: $$p_1 + p_2 + ... + p_s = q_1 + q_2 + ... + q_t$$(a) Show that the biggest ally of any positive integer has to have only $2$ and $3$ in its prime factorization. (b) Find the biggest number which is allied of $2021$ .