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A033833
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Highly factorable numbers: numbers with a record number of proper factorizations.
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34
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1, 4, 8, 12, 16, 24, 36, 48, 72, 96, 120, 144, 192, 216, 240, 288, 360, 432, 480, 576, 720, 960, 1080, 1152, 1440, 2160, 2880, 4320, 5040, 5760, 7200, 8640, 10080, 11520, 12960, 14400, 15120, 17280, 20160, 25920, 28800, 30240, 34560
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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Factorizations of the initial terms:
() (4) (8) (12) (16) (24) (36) (48)
(2*2) (2*4) (2*6) (2*8) (3*8) (4*9) (6*8)
(2*2*2) (3*4) (4*4) (4*6) (6*6) (2*24)
(2*2*3) (2*2*4) (2*12) (2*18) (3*16)
(2*2*2*2) (2*2*6) (3*12) (4*12)
(2*3*4) (2*2*9) (2*3*8)
(2*2*2*3) (2*3*6) (2*4*6)
(3*3*4) (3*4*4)
(2*2*3*3) (2*2*12)
(2*2*2*6)
(2*2*3*4)
(2*2*2*2*3)
(End)
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MATHEMATICA
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nn=100;
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
qv=Table[Length[facs[n]], {n, nn}];
Table[Position[qv, i][[1, 1]], {i, qv//.{foe___, x_, y_, afe___}/; x>=y:>{foe, x, afe}}] (* Gus Wiseman, Jan 13 2020 *)
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CROSSREFS
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The corresponding records are A272691.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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