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A370584
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Number of subsets of {1..n} such that only one set can be obtained by choosing a different prime factor of each element.
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21
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1, 1, 2, 4, 6, 12, 18, 36, 48, 68, 104, 208, 284, 568, 888, 1296, 1548, 3096, 3968
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OFFSET
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0,3
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COMMENTS
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For example, the only choice of a different prime factor of each element of (4,5,6) is (2,5,3).
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LINKS
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EXAMPLE
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The a(0) = 1 through a(6) = 18 subsets:
{} {} {} {} {} {} {}
{2} {2} {2} {2} {2}
{3} {3} {3} {3}
{2,3} {4} {4} {4}
{2,3} {5} {5}
{3,4} {2,3} {2,3}
{2,5} {2,5}
{3,4} {2,6}
{3,5} {3,4}
{4,5} {3,5}
{2,3,5} {3,6}
{3,4,5} {4,5}
{4,6}
{2,3,5}
{2,5,6}
{3,4,5}
{3,5,6}
{4,5,6}
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MATHEMATICA
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Table[Length[Select[Subsets[Range[n]], Length[Union[Sort/@Select[Tuples[If[#==1, {}, First/@FactorInteger[#]]&/@#], UnsameQ@@#&]]]==1&]], {n, 0, 10}]
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CROSSREFS
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Maximal sets of this type are counted by A370585.
A355741 counts ways to choose a prime factor of each prime index.
Cf. A000040, A000720, A003963, A005117, A045778, A133686, A307984, A355739, A355744, A355745, A367905.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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