A hoax number is a composite number defined analogously to a Smith number except that its decimal digit sum equals the sum of the decimal digit sums of its distinct prime factors (excluding 1).
The first few hoax numbers are 22, 58, 84, 85, 94, 136, 160, 166, 202, 234, ... (OEIS A019506), illustrated above as a binary plot, and the corresponding digit sums are 4, 13, 12, 13, 13, 10, 7, 13, 4, 9, 7, ... (OEIS A050223).
