I dreamed the other night that my brother studied "Smith numbers" and that these numbers had something to do with medicine.

I've never heard of "Smith numbers" before.

So I looked them up on Google, feeling pretty sure there was no such thing.

Behold my error:

http://www.math.eku.edu/PJCostello/smith.htm

Smith Numbers

One interesting property of some positive integers came into existence because of a phone call. In 1982, Harold Smith called his brother-in-law, mathematician Albert Wilansky of Lehigh University, with the observation that his phone number was composite and the sum of the digits in the phone number equals the sum of the digits in its prime factors. Wilansky published this observation [6] and it was the birth of Smith numbers.

We introduce two arithmetic functions and then restate the definition of Smith numbers in terms of these two functions. Let S(N) represent the sum of the digits in N. Let Sp(N) represent the sum of the digits in the primes in the factorization of N. For example, Sp(12) = Sp(2*2*3) = 2+2+3 =7.

Definition. A composite integer N is called Smith if S(N) = Sp(N).

Well, I don't know what all this means, nor do I know what they have to do with medicine.