A068316 Run lengths of the Moebius function applied to A051270 (numbers with 5 distinct prime factors).

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, 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, 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

Offset: 1

Author

Jani Melik, Feb 26 2002

Keywords

• nonn

Examples

			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.
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, ...
		

Crossrefs

Cf. A046387, A051270.

Programs

Maple

runl := 1 :
for n from 2 to 1000 do
    if numtheory[mobius](A051270(n)) = numtheory[mobius](A051270(n-1)) then
        runl := runl+1 ;
    else
        printf("%d,",runl) ;
        runl := 1;
    end if;
end do: # R. J. Mathar, Oct 13 2019

Extensions

Corrected and extended by R. J. Mathar, Oct 13 2019