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%I #6 Jul 12 2019 20:19:48
%S 1,1,1,1,1,1,1,2,1,1,1,3,1,1,1,2,1,3,1,3,1,1,1,3,1,1,2,3,1,4,1,3,1,1,
%T 1,3,1,1,1,3,1,4,1,3,3,1,1,5,1,3,1,3,1,3,1,3,1,1,1,4,1,1,3,4,1,4,1,3,
%U 1,4,1,6,1,1,3,3,1,4,1,5,2,1,1,4,1,1,1
%N Number of factorizations of n into factors > 1 where each factor has a different number of prime factors counted with multiplicity.
%H Gus Wiseman, <a href="/A038041/a038041.txt">Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.</a>
%e The a(96) = 8 factorizations: (2*4*12), (2*6*8), (2*48), (3*4*8), (3*32), (4*24), (6*16), (96).
%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],UnsameQ@@PrimeOmega/@#&]],{n,100}]
%Y Cf. A001055, A007837, A038041, A321455, A321469, A322794, A326026, A326515, A326516, A326517, A326533.
%K nonn
%O 1,8
%A _Gus Wiseman_, Jul 11 2019
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