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A322438
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Number of unordered pairs of factorizations of n into factors > 1 where no factor of one properly divides any factor of the other.
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4
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0
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OFFSET
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1
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COMMENTS
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LINKS
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EXAMPLE
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The a(240) = 5 pairs of factorizations::
(4*4*15)|(4*6*10)
(6*40)|(15*16)
(8*30)|(12*20)
(10*24)|(15*16)
(12*20)|(15*16)
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MATHEMATICA
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facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
divpropQ[x_, y_]:=And[x!=y, Divisible[x, y]];
Table[Length[Select[Subsets[facs[n], {2}], And[!Or@@divpropQ@@@Tuples[#], !Or@@divpropQ@@@Reverse/@Tuples[#]]&]], {n, 100}]
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CROSSREFS
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Cf. A001055, A285572, A285573, A303362, A303386, A304713, A305149, A305150, A305193, A316476, A317144, A322435, A322436, A322437, A322442.
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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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