A Smith number is a number which in a given base, the sum of its digits is
equal to the sum of the digits in its factorization. (In the case of numbers that
are not square-free, the factorization is written without exponents, writing the
repeated factor as many times as needed). For example, 202 is a Smith number,
since 2 + 0 + 2 = 4, and its factorization is 2 101, and 2 + 1 + 0 + 1 = 4.