Editing Smith number (section)

==Mathematical definition==
Let <math>n</math> be a [[natural number]]. For base <math>b > 1</math>, let the function <math>F_b(n)</math> be the [[digit sum]] of <math>n</math> in base <math>b</math>. A natural number <math>n</math> with prime factorization
<math display="block">
n = \prod_{\stackrel{p \mid n,}{p\text{ prime}}} p^{v_p(n)}
</math>
is a '''Smith number''' if
<math display="block">
F_b(n) = \sum_{{\stackrel{p \mid n,}{p\text{ prime}}}} v_p(n) F_b(p).
</math>
Here the exponent <math>v_p(n)</math> is the multiplicity of <math>p</math> as a prime factor of <math>n</math> (also known as the [[p-adic valuation|''p''-adic valuation]] of <math>n</math>).

For example, in base 10, 378 = 2<sup>1</sup> · 3<sup>3</sup> · 7<sup>1</sup> is a Smith number since 3 + 7 + 8 = 2&thinsp;·&thinsp;1 + 3&thinsp;·&thinsp;3 + 7&thinsp;·&thinsp;1, and 22 = 2<sup>1</sup> · 11<sup>1</sup> is a Smith number, because 2 + 2 = 2&thinsp;·&thinsp;1 + (1 + 1)&thinsp;·&thinsp;1.

The first few Smith numbers in base 10 are
:[[4 (number)|4]], [[22 (number)|22]], [[27 (number)|27]], [[58 (number)|58]], [[85 (number)|85]], [[94 (number)|94]], [[121 (number)|121]], [[166 (number)|166]], [[202 (number)|202]], [[265 (number)|265]], [[274 (number)|274]], [[319 (number)|319]], [[346 (number)|346]], [[355 (number)|355]], [[378 (number)|378]], [[382 (number)|382]], [[391 (number)|391]], [[438 (number)|438]], [[454 (number)|454]], [[483 (number)|483]], [[517 (number)|517]], [[526 (number)|526]], [[535 (number)|535]], [[562 (number)|562]], [[576 (number)|576]], [[588 (number)|588]], [[627 (number)|627]], [[634 (number)|634]], [[636 (number)|636]], [[645 (number)|645]], [[648 (number)|648]], [[654 (number)|654]], [[663 (number)|663]], [[666 (number)|666]], [[690 (number)|690]], [[706 (number)|706]], [[728 (number)|728]], [[729 (number)|729]], [[762 (number)|762]], [[778 (number)|778]], [[825 (number)|825]], [[852 (number)|852]], [[861 (number)|861]], [[895 (number)|895]], [[913 (number)|913]], [[915 (number)|915]], [[922 (number)|922]], [[958 (number)|958]], [[985 (number)|985]]. {{OEIS|id=A006753}}