Totient Valence Function

Author

Eric W. Weisstein
August 21, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/NumberTheoreticFunctions/TotientValenceFunction.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/TotientValenceFunction.html.

©2006 Wolfram Research, Inc. except for portions noted otherwise

Table of N having given ϕ(N)

ϕ=MapIndexed[{#1,#2[[1]]}&,EulerPhi[Range[1000]]];

(l={#[[1,1]],Last/@#}&/@Split[Select[Sort[ϕ],#[[1]]≤50&],#1[[1]]==#2[[1]]&])//ColumnForm

Length/@Last/@l

First/@l

all=Sort[Join[l,{#,{}}&/@Complement[Range[50],First/@l]]];

mult=Length/@Last/@all

#[[1,2]]&/@Rest[Split[Sort[MapIndexed[{#1,#2[[1]]}&,mult]],#1[[1]]==#2[[1]]&]]