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

1,2

Links

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

Formula

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

Example

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;

Mathematica

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

Prog

(Magma)
A277646:=func<n, k|n^2 div k>;
[A277646(n, k):k in[1..n^2], n in[1..7]];

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).

Sequence in context: A051568 A016509 A332630 * A337271 A010313 A159823

Adjacent sequences: A277643 A277644 A277645 * A277647 A277648 A277649

Keyword

nonn,tabf,easy

Author

Jason Kimberley, Nov 09 2016

Status

approved