%I #11 Apr 10 2021 05:53:33

%S 0,0,0,0,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,

%T 1,1,0,0,1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,

%U 2,1,0,1,1,1,1,1,1,0,1,2,0,1,1,0,1,0,1,1,0,1,1,0,0,1,1,0,1,1,1,0,1,1,0,2,0

%N Number of gaps in factors of the n-th squarefree number.

%H Amiram Eldar, <a href="/A073484/b073484.txt">Table of n, a(n) for n = 1..10000</a>

%F a(A000040(n))=0; a(A006094(n))=0; a(A002110(n))=0; a(A073485(n))=0.

%F a(A073486(n))>0; a(A073487(n))=1; a(A073488(n))=2; a(A073489(n))=3.

%F a(n)=0 iff A073483(n)=1.

%e The 69th squarefree number is 110=2*5*11, therefore a(69)=2, as there are two gaps: between 2 and 5 and between 5 and 11.

%t gaps[n_] := SequenceCount[FactorInteger[n][[;; , 1]], {p1_, p2_} /; p2 != NextPrime[p1], Overlaps -> True]; gaps /@ Select[Range[200], SquareFreeQ] (* _Amiram Eldar_, Apr 10 2021 *)

%Y Cf. A005117, A073483.

%K nonn

%O 1,69

%A _Reinhard Zumkeller_, Aug 03 2002