Definition:Smith Number/Historical Note

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Historical Note on Smith Number

The term Smith number was coined by Albert Wilansky.

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: $4937775$!


Sources

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