A277647 Triangle T(n,k) = floor(n/sqrt(k)) for 1 <= k <= n^2, read by rows.

1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 4, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 4, 4, 3, 3, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Author

Jason Kimberley, Nov 09 2016

Keywords

• nonn
• tabf
• easy

Examples

			The first five rows of the triangle are:
1;
2, 1, 1, 1;
3, 2, 1, 1, 1, 1, 1, 1, 1;
4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
5, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 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. A010766, A277646, A277648.

The 1000th row is A033432.

Programs

Magma

A277647:=func;
[A277647(n,k):k in[1..n^2],n in[1..7]];

Mathematica

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

PARI

row(n) = for(k=1, n^2, print1(floor(n/sqrt(k)), ", ")); print("")
trianglerows(n) = for(k=1, n, row(k))
/* Print initial five rows of triangle as follows: */
trianglerows(5) \\ Felix Fröhlich, Nov 12 2016

Formula

T(n,k) = A000196(A277646(n,k)).

T(n,k)sqrt(k) <= n < (T(n,k)+1)sqrt(k).