%I #5 Sep 23 2019 13:41:24

%S 1,1,1,2,1,2,1,2,2,2,1,3,1,2,2,3,1,3,1,3,2,2,1,3,2,2,2,3,1,5,1,2,2,2,

%T 2,6,1,2,2,3,1,5,1,3,3,2,1,4,2,3,2,3,1,3,2,3,2,2,1,7,1,2,3,4,2,5,1,3,

%U 2,5,1,5,1,2,3,3,2,5,1,4,3,2,1,7,2,2,2

%N Number of factorizations of n that are constant or whose distinct factors are pairwise coprime.

%C First differs from A327400 at A327400(24) = 4, a(24) = 3.

%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) = A327695(n) + A089723(n).

%e The a(90) = 7 factorizations together with the corresponding multiset partitions of {1,2,2,3}:

%e (2*3*3*5) {{1},{2},{2},{3}}

%e (2*5*9) {{1},{3},{2,2}}

%e (2*45) {{1},{2,2,3}}

%e (3*3*10) {{2},{2},{1,3}}

%e (5*18) {{3},{1,2,2}}

%e (9*10) {{2,2},{1,3}}

%e (90) {{1,2,2,3}}

%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],Length[Union[#]]==1||CoprimeQ@@Union[#]&]],{n,100}]

%Y Constant factorizations are A089723.

%Y Partitions whose distinct parts are pairwise coprime are A304709.

%Y Factorizations that are constant or relatively prime are A327400.

%Y See link for additional cross-references.

%Y A007359, A050320, A051424, A281116, A302569, A302696, A304711.

%K nonn

%O 1,4

%A _Gus Wiseman_, Sep 22 2019