A totient is a sequence f:{1,2,3,} such that


for some two completely multiplicative sequences g and h, where denotes the convolution productPlanetmathPlanetmath (or Dirichlet product; see multiplicative function).

The term ‘totient’ was introduced by Sylvester in the 1880’s, but is seldom used nowadays except in two cases. The Euler totient ϕ satisfies


where ιk denotes the functionMathworldPlanetmath nnk (which is completely multiplicative). The more general Jordan totient Jk is defined by

Title totient
Canonical name Totient
Date of creation 2013-03-22 13:38:35
Last modified on 2013-03-22 13:38:35
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 5
Author mathcam (2727)
Entry type Definition
Classification msc 11A25
Defines totient
Defines Jordan totient