A278101 Triangle T(n,k) = A277648(n,k)^2 * A005117(k), read by rows.

1, 4, 2, 3, 9, 8, 3, 5, 6, 7, 16, 8, 12, 5, 6, 7, 10, 11, 13, 14, 15, 25, 18, 12, 20, 24, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 36, 32, 27, 20, 24, 28, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 49, 32, 48, 45, 24, 28, 40, 44, 13, 14, 15, 17, 19, 21, 22

Offset: 1

Author

Jason Kimberley, Nov 15 2016

Keywords

• nonn
• tabf
• easy

Comments

Other that the first (with length 1), row n has length A278100(n).

Equivalently, the surd sqrt(T(n,k)) = A277648(n,k) * sqrt(A005117(k)).

Examples

			The first five rows are:
1;
4,  2,  3;
9,  8,  3,  5,  6,  7;
16,  8, 12,  5,  6,  7, 10, 11, 13, 14, 15;
25, 18, 12, 20, 24,  7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23;
		

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..10716 (the first 37 rows of the triangle)

Crossrefs

Cf. A278103.

Programs

Magma

A277647:=func;
A278101_row:=funcA277647(n,j):j in[1..n^2]|IsSquarefree(j)]>;
&cat[A278101_row(n):n in[1..8]];

Mathematica

DeleteCases[#, 0] & /@ Table[Boole[SquareFreeQ@ k] k Floor[n/Sqrt@ k]^2, {n, 7}, {k, n^2}] // Flatten (* Michael De Vlieger, Nov 24 2016 *)