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A347262
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Positive integers that are not the numbers k for which the symmetric representation of sigma(k) has two parts, each of width one.
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1
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1, 2, 4, 6, 8, 9, 12, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 33, 35, 36, 39, 40, 42, 45, 48, 49, 50, 51, 54, 55, 56, 57, 60, 63, 64, 65, 66, 69, 70, 72, 75, 77, 78, 80, 81, 84, 85, 87, 88, 90, 91, 93, 95, 96, 98, 99, 100, 102, 104, 105, 108, 110, 111, 112, 114
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OFFSET
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1,2
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COMMENTS
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First differs from A071562 at a(12) = 21 here, there a(12) = 24.
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LINKS
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EXAMPLE
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6 is in the sequence because the symmetric representation of sigma(6) has only one part. The 11 widths of 6 are [1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1]. The sum of them is A000203(6) = 12.
9 is in the sequence because the symmetric representation of sigma(9) has three parts. The 17 widths of 9 are [1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1]. The sum of them is A000203(9) = 13.
78 is in the sequence because the symmetric representation of sigma(78) has two parts but not all their widths are one since 14 widths are two. The 155 widths of 78 are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], the same as the 78th row of A249351. The sum of the widths is equal to A000203(78) = 168.
14 is not in the sequence because the symmetric representation of sigma(14) has two parts, each of width one. The 27 widths of 14 are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], the same as the 14th row of A249351. The sum of the widths is equal to A000203(14) = 24.
For the definition of "width" see A249351.
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MATHEMATICA
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(* functions a237048 and a237270 are defined in the respective sequences *)
a249223[n_] :=Drop[FoldList[Plus, 0, Map[(-1)^(#+1) a237048[n, #]&, Range[row[n]]]], 1]
a347262[n_] := Select[Range[n], Length[a237270[#]]!=2||Max[a249223[#]]!=1&]
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CROSSREFS
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Cf. A000203, A071562, A196020, A236104, A237270, A237271, A237591, A237593, A245092, A246955 (complement), A249351 (widths).
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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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