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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
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.
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<n, k|Isqrt(n^2 div k)>;
A278101_row:=func<n|[a^2*k where a is A277647(n, k):k in[1..n^2]|IsSquarefree(k)]>;
A278103_row:=func<n|(exists(dec){row[1..j]:j in[1..#row-1]|row[j]le row[j+1]}select dec else[1]) where row is A278101_row(n) >;
&cat[A278103_row(n):n in[1..23]];
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Jason Kimberley, Nov 15 2016
STATUS
approved