A277646 Triangle T(n,k) = floor(n^2/k) for 1 <= k <= n^2, read by rows.

1, 4, 2, 1, 1, 9, 4, 3, 2, 1, 1, 1, 1, 1, 16, 8, 5, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 25, 12, 8, 6, 5, 4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 36, 18, 12, 9, 7, 6, 5, 4, 4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 49, 24, 16, 12, 9, 8, 7, 6

Offset: 1

Author

Jason Kimberley, Nov 09 2016

Keywords

• nonn
• tabf
• easy

Examples

			The first five rows of the triangle are:
1;
4, 2, 1, 1;
9, 4, 3, 2, 1, 1, 1, 1, 1;
16, 8, 5, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1;
25, 12, 8, 6, 5, 4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
		

Links

• Jason Kimberley, Table of n, a(n) for n = 1..10416 (the first 31 rows of the triangle)

Crossrefs

Cf. Related triangles: A010766, A277647, A277648.

Rows of this triangle (with infinite trailing zeros):

T(1,k) = A000007(k-1),

T(2,k) = A033324(k),

T(3,k) = A033329(k),

T(4,k) = A033336(k),

T(5,k) = A033345(k),

T(6,k) = A033356(k),

T(7,k) = A033369(k),

T(8,k) = A033384(k),

T(9,k) = A033401(k),

T(10,k) = A033420(k),

T(100,k) = A033422(k),

T(10^3,k) = A033426(k),

T(10^4,k) = A033424(k).

Columns of this triangle:

T(n,1) = A000290(n),

T(n,2) = A007590(n),

T(n,3) = A000212(n),

T(n,4) = A002620(n),

T(n,5) = A118015(n),

T(n,6) = A056827(n),

T(n,7) = A056834(n),

T(n,8) = A130519(n+1),

T(n,9) = A056838(n),

T(n,10)= A056865(n),

T(n,12)= A174709(n+2).

Programs

Magma

A277646:=func;
[A277646(n,k):k in[1..n^2],n in[1..7]];

Mathematica

Table[Floor[n^2/k], {n, 7}, {k, n^2}] // Flatten (* Michael De Vlieger, Nov 24 2016 *)

Formula

T(n,k) = A010766(n^2,k).