[[wp:Smith numbers|Smith numbers]] are numbers such that the [[Sum_digits_of_an_integer|sum of the decimal digits of the integers]] that make up that number is the same as the sum of the decimal digits of its prime factors excluding the number itself. 

By definition, all primes are ''excluded'' as they (naturally) satisfy this condition!

Smith numbers are also known as &nbsp; ''joke'' &nbsp; numbers.


;Example
Using the number '''166'''<br>
Find the prime factors of '''166''' which are: '''2''' x '''83'''<br>
Then, take those two prime factors and sum all their decimal digits: '''2 + 8 + 3''' which is '''13'''<br>
Then, take the decimal digits of '''166''' and add their decimal digits: '''1 + 6 + 6''' which is '''13'''<br>
Therefore, the number '''166''' is a Smith number.


;Task
Write a program to find all Smith numbers ''below'' 10000.


;See also
* from Wikipedia: &nbsp; [[https://en.wikipedia.org/wiki/Smith_number Smith number]].
* from MathWorld: &nbsp; [[http://mathworld.wolfram.com/SmithNumber.html Smith number]]. 
* from OEIS A6753: &nbsp; [[https://oeis.org/A006753 OEIS sequence A6753]].
* from OEIS A104170: &nbsp; [[https://oeis.org/A104170 Number of Smith numbers below 10^n]]. 
* from The Prime pages: &nbsp; [[http://primes.utm.edu/glossary/xpage/SmithNumber.html Smith numbers]].
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