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A362622
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One and numbers whose prime factorization has its greatest part at a middle position.
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9
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 43, 46, 47, 49, 50, 51, 53, 54, 55, 57, 58, 59, 61, 62, 64, 65, 67, 69, 71, 73, 74, 75, 77, 79, 81, 82, 83, 85, 86, 87, 89, 91
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OFFSET
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1,2
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LINKS
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EXAMPLE
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The prime factorization of 150 is 5*5*3*2, with middle parts {3,5}, so 150 is in the sequence.
The prime factorization of 90 is 5*3*3*2, with middle parts {3,3}, so 90 is not in the sequence.
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MATHEMATICA
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mpm[q_]:=MemberQ[If[OddQ[Length[q]], {Median[q]}, {q[[Length[q]/2]], q[[Length[q]/2+1]]}], Max@@q];
Select[Range[100], #==1||mpm[Flatten[Apply[ConstantArray, FactorInteger[#], {1}]]]&]
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CROSSREFS
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Partitions of this type are counted by A237824.
The version for median instead of middles is A362621, counted by A053263.
A362611 counts modes in prime factorization.
A362613 counts co-modes in prime factorization.
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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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