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A370583
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Number of subsets of {1..n} such that it is not possible to choose a different prime factor of each element.
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25
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0, 1, 2, 4, 10, 20, 44, 88, 204, 440, 908, 1816, 3776, 7552, 15364, 31240, 63744, 127488, 257592, 515184, 1036336, 2079312, 4166408, 8332816, 16709632, 33470464, 66978208, 134067488, 268236928, 536473856, 1073233840, 2146467680, 4293851680, 8588355424, 17177430640
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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The a(0) = 0 through a(5) = 20 subsets:
. {1} {1} {1} {1} {1}
{1,2} {1,2} {1,2} {1,2}
{1,3} {1,3} {1,3}
{1,2,3} {1,4} {1,4}
{2,4} {1,5}
{1,2,3} {2,4}
{1,2,4} {1,2,3}
{1,3,4} {1,2,4}
{2,3,4} {1,2,5}
{1,2,3,4} {1,3,4}
{1,3,5}
{1,4,5}
{2,3,4}
{2,4,5}
{1,2,3,4}
{1,2,3,5}
{1,2,4,5}
{1,3,4,5}
{2,3,4,5}
{1,2,3,4,5}
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MATHEMATICA
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Table[Length[Select[Subsets[Range[n]], Length[Select[Tuples[If[#==1, {}, First/@FactorInteger[#]]&/@#], UnsameQ@@#&]]==0&]], {n, 0, 10}]
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CROSSREFS
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For non-isomorphic multiset partitions we have A368097, complement A368098.
The complement is counted by A370582.
For a unique choice we have A370584.
For binary indices instead of factors we have A370637, complement A370636.
A355741 counts choices of a prime factor of each prime index.
Cf. A000040, A000720, A001055, A001414, A003963, A005117, A045778, A355739, A355745, A367867, A367905, A368187.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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