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%I #18 Dec 19 2017 02:38:16
%S 1,1,1,3,1,2,1,4,3,2,1,4,1,2,2,10,1,4,1,4,2,2,1,7,3,2,4,4,1,5,1,8,2,2,
%T 2,13,1,2,2,7,1,5,1,4,4,2,1,12,3,4,2,4,1,7,2,7,2,2,1,11,1,2,4,29,2,5,
%U 1,4,2,5,1,16,1,2,4,4,2,5,1,12,10,2,1,11
%N Number of twice-factorizations of n where the first factorization is constant, i.e., type (P,R,P).
%C a(n) is also the number of ways to choose a perfect divisor d|n and then a sequence of log_d(n) factorizations of d.
%e The a(16) = 10 twice-factorizations are (2*2*2*2), (2*2*4), (2*8), (4*4), (16), (2*2)*(2*2), (2*2)*(4), (4)*(2*2), (4)*(4), (2)*(2)*(2)*(2).
%t postfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[postfacs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t a[n_]:=Sum[Length[postfacs[n^(1/g)]]^g,{g,Divisors[GCD@@FactorInteger[n][[All,2]]]}];
%t Array[a,50]
%Y Cf. A000005, A001055, A052409, A052410, A279787, A281113, A284639, A295920, A295924, A295931, A295935.
%K nonn
%O 1,4
%A _Gus Wiseman_, Nov 30 2017