A249327 Rectangular array T(n,k) = f(n)*k^2, where f = A005117 (squarefree numbers); n, k >= 1; read by antidiagonals.

1, 4, 2, 9, 8, 3, 16, 18, 12, 5, 25, 32, 27, 20, 6, 36, 50, 48, 45, 24, 7, 49, 72, 75, 80, 54, 28, 10, 64, 98, 108, 125, 96, 63, 40, 11, 81, 128, 147, 180, 150, 112, 90, 44, 13, 100, 162, 192, 245, 216, 175, 160, 99, 52, 14, 121, 200, 243, 320, 294, 252, 250

Offset: 1

Author

Clark Kimberling, Oct 26 2014

Keywords

• nonn
• tabl
• easy

Comments

Every positive integer occurs exactly once.

Examples

			Northwest corner:
1   4    9    16   25    36    49
2   8    18   32   50    72    98
3   12   27   48   75    108   147
5   20   45   80   125   180   245
6   24   54   96   150   216   294
		

Crossrefs

Cf. A005117, A000037 (is partitioned by the rows of A249327, excluding the first).

Programs

Mathematica

z = 20; f = Select[Range[10000], SquareFreeQ[#] &];
u[n_, k_] := f[[n]]*k^2; t = Table[u[n, k], {n, 1, 20}, {k, 1, 20}];
TableForm[t] (* A249327 array *)
Table[u[k, n - k + 1], {n, 1, 15}, {k, 1, n}] // Flatten (* A249327 sequence *)

Formula

T(1,k) = A000290(k), T(2,k) = A001105(k), T(3,k) = A033428(k), T(4,k) = A033429(k), T(5,.) through T(10,.) are A033581, A033582, A033583, A033584, A152742 and A144555 without initial 0. - M. F. Hasler, Oct 31 2014