infinitary MoebiusMu

[Meeussen Wouter (bkarnd)]

sequel to "what is the value "60" doing in A000028 ??"

***********  
more simply, this 'different construction' is
***********
iMoebiusMu[n_]:=
    Switch[MoebiusMu[n],1,1,-1,-1,0,
 
If[OddQ[Plus@@(DigitCount[Last[Transpose[FactorInteger[n]]],2,1])],-1,1]];
iMoebiusMu[1]:=1;

which says simply that iMu[n]= Mu[n] if Mu[n]<>0,
and if Mu[n]=0, then iMu[n] is -1 iff the sum of the binary digits of the
prime exponents
 (in its prime decomposition) is odd.


And yet the Moebius inversion formula seems to (also) hold for these iMu[].

Cute, no?


Wouter Meeussen
tel  +32 (0)51 332 124
fax +32 (0)51 332 175
mail: wouter.meeussen at vandemoortele.com




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