Liouville function

The Liouville functionDlmfMathworldPlanetmath is defined by λ(1)=1 and λ(n)=(-1)k1+k2++kr, if the prime factorizationMathworldPlanetmath of n>1 is n=p1k1p2k2prkr (where each pi is positive). This functionMathworldPlanetmath is completely multiplicative and the

d|nλ(d)={1if n=m2 for some integer m0otherwise,

where the sum runs over all positive divisorsMathworldPlanetmathPlanetmath of n.

Title Liouville function
Canonical name LiouvilleFunction
Date of creation 2013-03-22 11:47:09
Last modified on 2013-03-22 11:47:09
Owner KimJ (5)
Last modified by KimJ (5)
Numerical id 12
Author KimJ (5)
Entry type Definition
Classification msc 20G10
Classification msc 11A25
Classification msc 81-00