A278103 Irregular triangle T(n,k) := A278101(n,k) for k = 1..A278102(n), read by rows.

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

Author

Jason Kimberley, Nov 15 2016

Keywords

• nonn
• tabf
• easy

Comments

Each row is the longest strictly decreasing prefix of the corresponding row of A278101.

Examples

			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;
		

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)

Crossrefs

Cf. A005117, A278101, A278102, A278104.

Programs

Magma

A277647:=func;
A278101_row:=funcA277647(n,k):k in[1..n^2]|IsSquarefree(k)]>;
A278103_row:=funcA278101_row(n) >;
&cat[A278103_row(n):n in[1..23]];

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 *)

Formula

T(n,k) = A278104(n,k) * A005117(k) where this triangle and A278104 both have row length sequence A278102.