Definition:Smith Number/Historical Note

Historical Note on Smith Number
The term Smith number was coined by.

He noticed the property in the phone number ($493$ - $7775$) of his brother-in-law Harold Smith:
 * $4937775 = 3 × 5 × 5 × 65837$

while:
 * $4 + 9 + 3 + 7 + 7 + 7 + 5 = 3 + 5 + 5 + 6 + 5 + 8 + 3 + 7 = 42$

The full text of the article in which this appeared:


 * A Smith number is a composite number the sum of whose digits is the sum of all the digits of its prime factors. The (rather startling) reason for the name is mentioned below.


 * Examples. $9985 = 5 \times 1997$, $9 + 9 + 8 + 5 = 5 + 1 + 9 + 9 + 7$, $6036 = 2 \times 2 \times 3 \times 503$, $6 + 0 + 3 + 6 = 2 + 2 + 3 + 5 + 0 + 3$.


 * The number of Smith numbers between $n$ thousand and $n$ thousand $+ 999$ for $n = 0, 1, 2, \ldots, 9$, is, respectively, $47$, $32$, $42$, $28$, $33$, $32$, $32$, $37$, $37$, $40$.


 * I wonder whether there are infinitely many Smith numbers.


 * The largest Smith number known is due to my brother-in-law H. Smith who is not a mathematician. It is his telephone number: $4937775$!