A natural number n is called a Smith number if n is a composite for which the digital
sum S(n) equals the p-digit sum Sp(n), where Sp(n) is given by the digital sum of all the
prime factors of n, counting multiplicity. For example, based on the factorization
636 = 22 · 3 · 53, we have Sp(636) = 2 + 2 + 3 + 5 + 3 = 15. Since S(636) = 6 +
3 + 6 = 15, then S(636) = Sp(636) and therefore, 636 is a Smith number.