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A320511
Numbers k with the property that the symmetric representation of sigma(k) has six parts.
5
147, 171, 189, 207, 243, 261, 275, 279, 297, 333, 351, 363, 369, 387, 423, 429, 465, 477, 507, 531, 549, 555, 595, 603, 605, 615, 639, 645, 657, 663, 705, 711, 715, 741, 747, 795, 801, 833, 845, 867, 873, 885, 909, 915, 927, 931, 935, 963, 969, 981, 1005, 1017, 1045, 1065, 1071, 1083, 1095, 1105, 1127
OFFSET
1,1
COMMENTS
Those numbers in this sequence with only parts of width 1 in their symmetric representation of sigma form column 6 in the table of A357581. - Hartmut F. W. Hoft, Oct 04 2022
EXAMPLE
147 is in the sequence because the 147th row of A237593 is [74, 25, 13, 8, 5, 4, 4, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 4, 4, 5, 8, 13, 25, 74], and the 146th row of the same triangle is [74, 25, 12, 8, 6, 4, 3, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 4, 6, 8, 12, 25, 74], therefore between both symmetric Dyck paths there are six parts: [74, 26, 14, 14, 26, 74].
Note that the sum of these parts is 74 + 26 + 14 + 14 + 26 + 74 = 228, equaling the sum of the divisors of 147: 1 + 3 + 7 + 21 + 49 + 147 = 228.
(The diagram of the symmetric representation of sigma(147) = 228 is too large to include.)
MATHEMATICA
(* function a341969 and support functions are defined in A341969, A341970 and A341971 *)
partsSRS[n_] := Length[Select[SplitBy[a341969[n], #!=0&], #[[1]]!=0&]]
a320511[n_] := Select[Range[n], partsSRS[#]==6&]
a320511[1127] (* Hartmut F. W. Hoft, Oct 04 2022 *)
CROSSREFS
Column 6 of A240062.
Cf. A237270 (the parts), A237271 (number of parts), A174973 (one part), A239929 (two parts), A279102 (three parts), A280107 (four parts), A320066 (five parts).
Sequence in context: A145212 A195239 A122064 * A259288 A325608 A375155
KEYWORD
nonn,changed
AUTHOR
Omar E. Pol, Oct 14 2018
STATUS
approved