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%I #5 Sep 16 2018 21:36:32
%S 1,1,1,2,1,2,1,3,2,2,1,3,1,2,2,4,1,3,1,3,2,2,1,5,2,2,3,3,1,5,1,4,2,2,
%T 2,7,1,2,2,5,1,5,1,3,3,2,1,7,2,3,2,3,1,5,2,5,2,2,1,9,1,2,3,8,2,5,1,3,
%U 2,5,1,9,1,2,3,3,2,5,1,7,4,2,1,9,2,2,2
%N Number of uniform factorizations of n into factors > 1, where a factorization is uniform if all factors appear with the same multiplicity.
%F a(n) = Sum_{d|A052409(n)} A045778(n^(1/d)).
%e The a(144) = 17 factorizations:
%e (144),
%e (2*72), (3*48), (4*36), (6*24), (8*18), (9*16), (12*12),
%e (2*3*24), (2*4*18), (2*6*12), (2*8*9), (3*4*12), (3*6*8),
%e (2*2*6*6), (2*3*4*6), (3*3*4*4).
%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],SameQ@@Length/@Split[#]&]],{n,100}]
%Y Cf. A001055, A045778, A047966, A052409, A072774, A296132, A303386, A317710, A317712, A317717, A317718.
%K nonn
%O 1,4
%A _Gus Wiseman_, Sep 16 2018
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