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A322435
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Number of pairs of factorizations of n into factors > 1 where no factor of the second divides any factor of the first.
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9
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1, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 3, 0, 1, 1, 5, 0, 3, 0, 3, 1, 1, 0, 7, 1, 1, 2, 3, 0, 4, 0, 7, 1, 1, 1, 15, 0, 1, 1, 7, 0, 4, 0, 3, 3, 1, 0, 16, 1, 3, 1, 3, 0, 7, 1, 7, 1, 1, 0, 18, 0, 1, 3, 16, 1, 4, 0, 3, 1, 4, 0, 32, 0, 1, 3, 3, 1, 4, 0, 16, 5, 1, 0, 18, 1
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OFFSET
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1,8
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LINKS
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EXAMPLE
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The a(36) = 15 pairs of factorizations:
(2*2*3*3)|(4*9)
(2*2*3*3)|(6*6)
(2*2*3*3)|(36)
(2*2*9)|(6*6)
(2*2*9)|(36)
(2*3*6)|(4*9)
(2*3*6)|(36)
(2*18)|(36)
(3*3*4)|(6*6)
(3*3*4)|(36)
(3*12)|(36)
(4*9)|(6*6)
(4*9)|(36)
(6*6)|(4*9)
(6*6)|(36)
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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]]}]];
Table[Length[Select[Tuples[facs[n], 2], !Or@@Divisible@@@Tuples[#]&]], {n, 100}]
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CROSSREFS
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Cf. A000688, A001055, A050336, A265947, A294068, A305149, A305150, A305193, A317144, A322436, A322437, A322438, A322439, A322440, A322441, 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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