Difference between revisions of "Greatest prime factor"

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File:Gpfplot,n=0..100.png|Plot of $\mathrm{gpf}$ for $n=0,\ldots,100$.
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File:Greatestprimefactor,to1000.png|Graph of $\mathrm{gpf}$.
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File:Gpfplot,n=0..1000.png|Plot of $\mathrm{gpf}$ for $n=0,\ldots,1000$.
 
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File:Gpfplot,n=0..10000.png|Plot of $\mathrm{gpf}$ for $n=0,\ldots,10000$.
 
 
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=Properties=
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=References=
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{{:Number theory functions footer}}
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[[Category:SpecialFunction]]

Latest revision as of 06:34, 22 June 2016

Define the greatest prime factor function $\mathrm{gpf}\colon \mathbb{Z}^+ \rightarrow \mathbb{Z}^+$ by

$\mathrm{gpf}(n) = \{\mathrm{greatest \hspace{2pt} prime \hspace{2pt} factor \hspace{2pt} of \hspace{2pt}}n\}.$

  • Graph of $\mathrm{gpf}$.

Properties

References

Number theory functions
Chebthetathumb.png
Chebyshev $\vartheta$
Chebyshevpsithumb.png
Chebyshev $\psi$

Euler $\phi$

Greatest prime factor

Mangoldt
Mertensthumb.png
Mertens

Möbius
Liouvillelambdathumb.png
Liouville $\lambda$

Prime counting
Riemannsiegelzthumb.png
Riemann-Siegel $Z$
Riemannzetathumb.png
Riemann zeta
Divisorsumthumb.png
Sum of divisors

Totient
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