%I #4 Sep 20 2019 08:58:10

%S 1,0,0,0,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,1,0,1,0,1,0,4,0,0,1,1,

%T 1,1,0,1,1,1,0,4,0,1,1,1,0,1,0,1,1,1,0,1,1,1,1,1,0,4,0,1,1,0,1,4,0,1,

%U 1,4,0,1,0,1,1,1,1,4,0,1,0,1,0,4,1,1,1

%N Number of factorizations of n that are empty or have at least two factors, all of which are > 1 and pairwise coprime.

%H Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>

%F a(n > 1) = A259936(n) - 1 = A000110(A001221(n)) - 1.

%t facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];

%t Table[Length[Select[facs[n],#=={}||CoprimeQ@@#&]],{n,100}]

%Y See link for additional cross-references.

%Y Cf. A302569, A302696, A304711, A305079, A327076, A327392.

%K nonn

%O 1,30

%A _Gus Wiseman_, Sep 19 2019