Difference between revisions of "Greatest prime factor"

From specialfunctionswiki
Jump to: navigation, search
 
(2 intermediate revisions by the same user not shown)
Line 6: Line 6:
 
<div align="center">
 
<div align="center">
 
<gallery>
 
<gallery>
−
File:Gpfplot,n=0..100.png|Plot of $\mathrm{gpf}$ for $n=0,\ldots,100$.
+
File:Greatestprimefactor,to1000.png|Graph of $\mathrm{gpf}$.
−
File:Gpfplot,n=0..1000.png|Plot of $\mathrm{gpf}$ for $n=0,\ldots,1000$.
 
−
File:Gpfplot,n=0..10000.png|Plot of $\mathrm{gpf}$ for $n=0,\ldots,10000$.
 
 
</gallery>
 
</gallery>
 
</div>
 
</div>
 +
 +
=Properties=
 +
 +
=References=
 +
 +
{{:Number theory functions footer}}
  
 
[[Category:SpecialFunction]]
 
[[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
Retrieved from "http://specialfunctionswiki.org/index.php?title=Greatest_prime_factor&oldid=6614"