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%I #9 Jan 07 2020 09:08:25
%S 1,4,8,12,16,24,36,48,60,72,96,120,128,144,180,192,216,240,256,288,
%T 360,384,420,432,480,576,720,768,840,864,900,960,1024,1080,1152,1260,
%U 1440,1680,1728,1800,1920,2048,2160,2304,2520,2592,2880,3072,3360,3456,3600
%N Sorted list containing the least number with each possible nonzero number of factorizations into factors > 1.
%C This is the sorted list of positions of first appearances in A001055 of each element of the range (A045782).
%H R. E. Canfield, P. Erdős and C. Pomerance, <a href="http://math.dartmouth.edu/~carlp/PDF/paper39.pdf">On a Problem of Oppenheim concerning "Factorisatio Numerorum"</a>, J. Number Theory 17 (1983), 1-28.
%e Factorizations of n for n = 4, 8, 12, 16, 24, 36, 48, 60:
%e 4 8 12 16 24 36 48 60
%e 2*2 2*4 2*6 2*8 3*8 4*9 6*8 2*30
%e 2*2*2 3*4 4*4 4*6 6*6 2*24 3*20
%e 2*2*3 2*2*4 2*12 2*18 3*16 4*15
%e 2*2*2*2 2*2*6 3*12 4*12 5*12
%e 2*3*4 2*2*9 2*3*8 6*10
%e 2*2*2*3 2*3*6 2*4*6 2*5*6
%e 3*3*4 3*4*4 3*4*5
%e 2*2*3*3 2*2*12 2*2*15
%e 2*2*2*6 2*3*10
%e 2*2*3*4 2*2*3*5
%e 2*2*2*2*3
%t nn=1000;
%t facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t nds=Length/@Array[facs,nn];
%t Table[Position[nds,i][[1,1]],{i,First/@Gather[nds]}]
%Y All terms belong to A025487
%Y Includes all highly factorable numbers A033833.
%Y Factorizations are A001055, with image A045782.
%Y The least number with A045782(n) factorizations is A045783(n).
%Y The least number with n factorizations is A330973(n).
%Y The strict version is A330997.
%Y Cf. A001222, A002033, A007716, A045778, A318284, A325238, A330935, A330936, A330976, A330977, A330989, A330991, A330992.
%K nonn
%O 1,2
%A _Gus Wiseman_, Jan 06 2020
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