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 A278104 Irregular triangle T(n,k) := A277648(n,k) for k = 1...A278102(n), read by rows. 4
 1, 2, 1, 3, 2, 1, 4, 2, 5, 3, 2, 6, 4, 3, 2, 7, 4, 8, 5, 4, 3, 9, 6, 10, 7, 5, 11, 7, 12, 8, 6, 13, 9, 7, 5, 14, 9, 15, 10, 8, 6, 16, 11, 17, 12, 9, 18, 12, 19, 13, 10, 20, 14, 11, 8, 21, 14, 22, 15, 12, 9, 8, 23, 16, 13, 10, 9, 8, 24, 16, 13, 10, 9, 25, 17, 26, 18, 27, 19, 15, 28, 19 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This triangle lists the "descending sequences across ranks" of Eggleton et al. REFERENCES R. B. Eggleton, J. S. Kimberley and J. A. MacDougall, Square-free rank of integers, submitted. LINKS EXAMPLE The first 23 rows are: 1; 2,  1; 3,  2,  1; 4,  2; 5,  3,  2; 6,  4,  3,  2; 7,  4; 8,  5,  4,  3; 9,  6; 10,  7,  5; 11,  7; 12,  8,  6; 13,  9,  7,  5; 14,  9; 15, 10,  8,  6; 16, 11; 17, 12,  9; 18, 12; 19, 13, 10; 20, 14, 11,  8; 21, 14; 22, 15, 12,  9,  8; 23, 16, 13, 10,  9,  8; MATHEMATICA Map[Last, #, {2}] &@ Map[TakeWhile[FoldList[Function[s, Boole[s < 0] {First@ #2, Last@ #2}][First@ #2 - First@ #1] &, #], Total@ # > 0 &] &, #] &@ Map[DeleteCases[#, {0, 0}] &, Table[Boole[SquareFreeQ@ k] {k #^2, #} &@ Floor[n/Sqrt@ k], {n, 32}, {k, n^2}] ] // Flatten (* Michael De Vlieger, Nov 24 2016 *) PROG (Magma) A277647:=func; A277648_row:=func; A278101_row:=func; A278104_row:=func; &cat[A278104_row(n):n in[1..23]]; CROSSREFS Sequence in context: A337632 A057058 A334441 * A141672 A141671 A309596 Adjacent sequences:  A278101 A278102 A278103 * A278105 A278106 A278107 KEYWORD nonn,tabf,easy AUTHOR Jason Kimberley, Nov 15 2016 STATUS approved

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Last modified June 24 17:31 EDT 2021. Contains 345417 sequences. (Running on oeis4.)