Editing Smith number (section)

{{Short description|Type of composite integer}}
{{Infobox integer sequence
| named_after = Harold Smith ([[brother-in-law]] of Albert Wilansky)
| author = [[Albert Wilansky]]
| number = [[infinity]]
| first_terms = [[4 (number)|4]], [[22 (number)|22]], [[27 (number)|27]], [[58 (number)|58]], [[85 (number)|85]], [[94 (number)|94]], [[121 (number)|121]]
| OEIS = A006753
}}
In [[number theory]], a '''Smith number''' is a [[composite number]] for which, in a given [[radix|number base]], the [[digit sum|sum of its digits]] is equal to the sum of the digits in its [[prime factor]]ization in the same base.  In the case of numbers that are not [[Square-free integer|square-free]], the factorization is written without exponents, writing the repeated factor as many times as needed.

Smith numbers were named by [[Albert Wilansky]] of [[Lehigh University]], as he noticed the property in the phone number (493-7775) of his brother-in-law Harold Smith:
: 4937775&nbsp;=&nbsp;3 · 5 · 5 · 65837
while 
: 4&nbsp;+&nbsp;9&nbsp;+&nbsp;3&nbsp;+&nbsp;7&nbsp;+&nbsp;7&nbsp;+&nbsp;7&nbsp;+&nbsp;5&nbsp;= 3 + 5 + 5 + (6&nbsp;+&nbsp;5&nbsp;+&nbsp;8&nbsp;+&nbsp;3&nbsp;+&nbsp;7)
in [[base 10]].<ref name=CS383>Sándor & Crstici (2004) p.383</ref>