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A326082
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Number of maximal sets of pairwise indivisible divisors of n.
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2
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1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 5, 2, 3, 3, 5, 2, 5, 2, 5, 3, 3, 2, 8, 3, 3, 4, 5, 2, 7, 2, 6, 3, 3, 3, 9, 2, 3, 3, 8, 2, 7, 2, 5, 5, 3, 2, 12, 3, 5, 3, 5, 2, 8, 3, 8, 3, 3, 2, 15, 2, 3, 5, 7, 3, 7, 2, 5, 3, 7, 2, 15, 2, 3, 5, 5, 3, 7, 2, 12, 5, 3, 2, 15, 3
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OFFSET
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1,2
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COMMENTS
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Depends only on prime signature.
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LINKS
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EXAMPLE
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The maximal sets of pairwise indivisible divisors of n = 1, 2, 4, 8, 12, 24, 30, 32, 36, 48, 60 are:
1 1 1 1 1 1 1 1 1 1 1
2 2 2 12 24 30 2 36 48 60
4 4 2,3 2,3 5,6 4 2,3 2,3 2,15
8 3,4 3,4 2,15 8 2,9 3,4 3,20
4,6 3,8 3,10 16 3,4 3,8 4,30
4,6 2,3,5 32 4,18 4,6 5,12
6,8 6,10,15 9,12 6,8 2,3,5
8,12 12,18 3,16 3,4,5
4,6,9 6,16 4,5,6
8,12 3,4,10
12,16 6,15,20
16,24 10,12,15
12,15,20
12,20,30
4,6,10,15
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MATHEMATICA
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stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Rest[Subsets[Divisors[n]]], stableQ[#, Divisible]&]]], {n, 100}]
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CROSSREFS
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Cf. A001055, A051026, A067992, A096827, A143824, A285572, A285573, A303362, A305148, A305149, A316476, A325861, A326023, A326077.
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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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