joke number

A composite number defined analogously to a Smith number except that the sum of the number's digits equals the sum of the digits 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 sums of digits are 4, 13, 12, 13, 13, 10, 7, 13, 4, 9, 7, ... (OEIS A050223).