totient valence function

Given an integer n, count how many integers m in the set {n+1,n+2,n2} satisfy ϕ(m)=n. This is the totient valence of n, usually labelled Nϕ(n). (The only two special cases are 2 and 6, for which one has to look a little beyound n2).

Robert Carmichael conjectured that Nϕ(n)=1 never. Two sequences in Sloane’s OEIS that list numbers with higher totient valences than preceding numbers are A007374 and A097942.

Title totient valence functionMathworldPlanetmath
Canonical name TotientValenceFunction
Date of creation 2013-03-22 15:50:57
Last modified on 2013-03-22 15:50:57
Owner CompositeFan (12809)
Last modified by CompositeFan (12809)
Numerical id 5
Author CompositeFan (12809)
Entry type Definition
Classification msc 11A25