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Run lengths of the Moebius function applied to A051270 (numbers with 5 distinct prime factors).
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%I #15 Oct 14 2019 01:29:26

%S 5,1,1,1,6,2,4,3,4,1,2,1,6,2,1,1,1,1,1,2,1,1,2,1,2,2,2,1,3,2,2,1,2,1,

%T 3,1,2,1,3,2,2,1,1,1,1,1,4,1,2,2,3,1,2,5,2,2,1,1,2,4,1,1,2,1,1,2,1,1,

%U 3,1,2,2,4,1,2,2,2,1,4,2,2,1,2,2,2,1,2,1,2,1,1,1,3,1,1,1,1,2

%N Run lengths of the Moebius function applied to A051270 (numbers with 5 distinct prime factors).

%e If we consider A051270 and apply the Moebius function mu(n) to it we get a sequence of values: (-1,-1,-1,-1,-1),0,(-1),0,(-1,-1,-1,-1,-1,-1),0,0,(-1,-1,-1,-1),0,0,0,(-1,-1,-1,-1),0,(-1,-1),0,(-1, ... If we then look at the lengths of runs of equal terms, we get the sequence.

%e If we consider the values of A051270 which are not in A046387 we get numbers which are not squarefree, so mu(A051270(.)) is zero: 4620, 5460, 6930, ...

%p runl := 1 :

%p for n from 2 to 1000 do

%p if numtheory[mobius](A051270(n)) = numtheory[mobius](A051270(n-1)) then

%p runl := runl+1 ;

%p else

%p printf("%d,",runl) ;

%p runl := 1;

%p end if;

%p end do: # _R. J. Mathar_, Oct 13 2019

%Y Cf. A046387, A051270.

%K nonn

%O 1,1

%A _Jani Melik_, Feb 26 2002

%E Corrected and extended by _R. J. Mathar_, Oct 13 2019