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

1,1

Links

Table of n, a(n) for n=1..98.

Example

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, ...

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

Crossrefs

Cf. A046387, A051270.

Sequence in context: A365403 A035316 A293718 * A359945 A284252 A284254

Adjacent sequences: A068313 A068314 A068315 * A068317 A068318 A068319

Keyword

nonn

Author

Jani Melik, Feb 26 2002

Extensions

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

Status

approved