A347262 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

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.

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 *)

CROSSREFS

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

Cf. A237048, A249223.

Sequence in context: A331936 A364123 A244799 * A367224 A316350 A335127

Adjacent sequences: A347259 A347260 A347261 * A347263 A347264 A347265

KEYWORD

nonn

AUTHOR

Omar E. Pol, Aug 28 2021

STATUS

approved