NumberTheory
InverseTotient
inverse of Euler's totient function
Calling Sequence
Parameters
Description
Examples
Compatibility
InverseTotient(m)
m
-
positive integer
The InverseTotient function returns the inverse image of Euler's totient function.
Given a positive integer m, InverseTotient(m) returns the set of integers n that satisfy the equation Totient(n) = m.
withNumberTheory:
InverseTotient1
1,2
InverseTotient8
15,16,20,24,30
mapTotient,15,16,20,24,30
8
There are no numbers besides 1 and 2 with an odd totient.
InverseTotient3unionInverseTotient2347
∅
`union`seqInverseTotienti,i=3..99,2
The following command plots the points (m, n), where n is a member of InverseTotient(m), for m from 1 to 1000.
plots:-pointplot`union`seqmapn↦m,n,InverseTotientm,m=1..1000,labels=m,InverseTotient(m),labeldirections=horizontal,vertical,color=Fuchsia,symbol=circle
The NumberTheory[InverseTotient] command was introduced in Maple 2016.
For more information on Maple 2016 changes, see Updates in Maple 2016.
See Also
NumberTheory[Totient]
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