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%I A045783 #11 Jan 11 2020 21:49:25
%S A045783 1,4,8,12,16,24,36,60,48,128,72,96,120,256,180,144,192,216,420,240,
%T A045783 1024,384,288,360,2048,432,480,900,768,840,576,1260,864,720,8192,960,
%U A045783 1080,1152,4620,1800,3072,1680,1728,1920,1440,32768,2304,2592,6144
%N A045783 Least value with A045782(n) factorizations.
%H A045783 Wikipedia, <a href="https://en.wikipedia.org/wiki/Multiplicative_partition">Multiplicative partition</a>
%H A045783 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 A045783 From _Gus Wiseman_, Jan 11 2020: (Start)
%e A045783 Factorizations of n = 1, 4, 8, 12, 16, 24, 36, 60, 48:
%e A045783   {}  4    8      12     16       24       36       60       48
%e A045783       2*2  2*4    2*6    2*8      3*8      4*9      2*30     6*8
%e A045783            2*2*2  3*4    4*4      4*6      6*6      3*20     2*24
%e A045783                   2*2*3  2*2*4    2*12     2*18     4*15     3*16
%e A045783                          2*2*2*2  2*2*6    3*12     5*12     4*12
%e A045783                                   2*3*4    2*2*9    6*10     2*3*8
%e A045783                                   2*2*2*3  2*3*6    2*5*6    2*4*6
%e A045783                                            3*3*4    3*4*5    3*4*4
%e A045783                                            2*2*3*3  2*2*15   2*2*12
%e A045783                                                     2*3*10   2*2*2*6
%e A045783                                                     2*2*3*5  2*2*3*4
%e A045783                                                              2*2*2*2*3
%e A045783 (End)
%Y A045783 All terms belong to A025487.
%Y A045783 The strict version is A045780.
%Y A045783 The sorted version is A330972.
%Y A045783 Includes all highly factorable numbers A033833.
%Y A045783 The least number with exactly n factorizations is A330973(n).
%Y A045783 Factorizations are A001055 with image A045782 and complement A330976.
%Y A045783 Strict factorizations are A045778 with image A045779 and complement A330975.
%Y A045783 Cf. A070175, A318284, A325238, A330974, A330989, A330992, A330998.
%K A045783 nonn
%O A045783 1,2
%A A045783 _David W. Wilson_

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