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

1,2

Links

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

Formula

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

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

Example

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;

Mathematica

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

Prog

(Magma)
A277647:=func<n, k|Isqrt(n^2 div k)>;
[A277647(n, k):k in[1..n^2], n in[1..7]];
(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

Crossrefs

Cf. A010766, A277646, A277648.

The 1000th row is A033432.

Sequence in context: A145037 A267115 A328919 * A296134 A306694 A158052

Adjacent sequences: A277644 A277645 A277646 * A277648 A277649 A277650

Keyword

nonn,tabf,easy

Author

Jason Kimberley, Nov 09 2016

Status

approved