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 A278103 Irregular triangle T(n,k) := A278101(n,k) for k = 1..A278102(n), read by rows. 4
 1, 4, 2, 9, 8, 3, 16, 8, 25, 18, 12, 36, 32, 27, 20, 49, 32, 64, 50, 48, 45, 81, 72, 100, 98, 75, 121, 98, 144, 128, 108, 169, 162, 147, 125, 196, 162, 225, 200, 192, 180, 256, 242, 289, 288, 243, 324, 288, 361, 338, 300, 400, 392, 363, 320, 441, 392, 484, 450, 432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Each row is the longest strictly decreasing prefix of the corresponding row of A278101. REFERENCES R. B. Eggleton, J. S. Kimberley and J. A. MacDougall, Square-free rank of integers, submitted. LINKS Jason Kimberley, Table of n, a(n) for n = 1..10001 (the first 3304 rows of the triangle) FORMULA T(n,k) = A278104(n,k) * A005117(k) where this triangle and A278104 both have row length sequence A278102. EXAMPLE The first 23 rows are: 1; 4, 2; 9, 8, 3; 16, 8; 25, 18, 12; 36, 32, 27, 20; 49, 32; 64, 50, 48, 45; 81, 72; 100, 98, 75; 121, 98; 144, 128, 108; 169, 162, 147, 125; 196, 162; 225, 200, 192, 180; 256, 242; 289, 288, 243; 324, 288; 361, 338, 300; 400, 392, 363, 320; 441, 392; 484, 450, 432, 405, 384; 529, 512, 507, 500, 486, 448; MATHEMATICA Map[TakeWhile[FoldList[Function[s, Boole[s < 0] #2][#2 - #1] &, #], # > 0 &] &, #] &@ Map[DeleteCases[#, 0] &, Table[Boole[SquareFreeQ@ k] k Floor[n/Sqrt@ k]^2, {n, 23}, {k, n^2}] ] // Flatten (* Michael De Vlieger, Nov 24 2016 *) PROG (Magma) A277647:=func; A278101_row:=func; A278103_row:=func; &cat[A278103_row(n):n in[1..23]]; CROSSREFS Cf. A005117, A278101, A278102, A278104. Sequence in context: A365255 A243968 A104583 * A249327 A182728 A290538 Adjacent sequences: A278100 A278101 A278102 * A278104 A278105 A278106 KEYWORD nonn,tabf,easy AUTHOR Jason Kimberley, Nov 15 2016 STATUS approved

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Last modified August 14 05:41 EDT 2024. Contains 375146 sequences. (Running on oeis4.)