A347262 Positive integers that are not the numbers k for which the symmetric representation of sigma(k) has two parts, each of width one.

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

Offset: 1

Author

Omar E. Pol, Aug 28 2021

Keywords

• nonn

Comments

First differs from A071562 at a(12) = 21 here, there a(12) = 24.

Examples

			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.
		

Crossrefs

Cf. A000203, A071562, A196020, A236104, A237270, A237271, A237591, A237593, A245092, A246955 (complement), A249351 (widths).

Cf. A237048, A249223.

Programs

Mathematica

(* 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&]
a347262[114] (* Hartmut F. W. Hoft, Jul 20 2022 *)