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%I #4 Jan 11 2020 15:27:14
%S 1,1,2,2,3,4,5,4,7,5,7,9,12,7,11,11,16,11,19,16,21,15,29,11,12,26,30,
%T 15,31,38,22,21,47,26,29,52,45,36,57,26,64,19,30,52,77,52,36,57,98,21,
%U 67,38,74,97,66,105,47,42,36,109,118,98,92,109,52,171,30
%N Number of factorizations of A055932(n), the least representative of the n'th distinct unsorted prime signature, into factors > 1.
%C A factorization of n is a finite, nondecreasing sequence of positive integers > 1 with product n. Factorizations are counted by A001055.
%C The unsorted prime signature of A055932(n) is given by row n of A124829.
%F a(n) = A001055(A055932(n)).
%e The a(1) = 1 through a(11) = 7 factorizations:
%e {} 2 4 6 8 12 16 18 24 30 32
%e 2*2 2*3 2*4 2*6 2*8 2*9 3*8 5*6 4*8
%e 2*2*2 3*4 4*4 3*6 4*6 2*15 2*16
%e 2*2*3 2*2*4 2*3*3 2*12 3*10 2*2*8
%e 2*2*2*2 2*2*6 2*3*5 2*4*4
%e 2*3*4 2*2*2*4
%e 2*2*2*3 2*2*2*2*2
%t facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t Length@*facs/@First/@GatherBy[Range[1500],If[#==1,{},Last/@FactorInteger[#]]&]
%Y The sorted-signature version is A050322.
%Y This sequence has range A045782.
%Y Factorizations are A001055.
%Y Cf. A025487, A033833, A045778, A045783, A070175, A181821, A325238, A330972, A330973, A330976, A330989, A330990, A330998, A331050.
%K nonn
%O 1,3
%A _Gus Wiseman_, Jan 10 2020
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