A277648 Triangle T(n,k) = A277647(n, A005117(k)), read by rows.

1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 5, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 4, 4, 3, 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, 8, 5, 4, 3, 3, 3, 2, 2, 2, 2, 2, 1

Offset: 1

Author

Jason Kimberley, Nov 10 2016

Keywords

• nonn
• tabf
• easy

Comments

The columns of this triangle are the columns of A277647 with squarefree index.

Other that the first (with length 1), row n has length A278100(n).

Examples

			Triangle begins:
1;
2, 1, 1;
3, 2, 1, 1, 1, 1;
4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1;
...
where the first 11 terms of A005117(k) are
1, 2, 3, 5, 6, 7,10,11,13,14,15.
		

Links

• Jason Kimberley, Table of n, a(n) for n = 1..10716 (the first 37 rows of the triangle)

Crossrefs

Cf. A277646, A277647.

Programs

Magma

A277647:=func;
A277648_row:=funcA277647(n,k):k in[1..n^2]|IsSquarefree(k)]>;
&cat[A277648_row(n):n in[1..8]];

Mathematica

DeleteCases[#, 0] & /@ Table[Boole[SquareFreeQ@ k] Floor[n/Sqrt@ k], {n, 8}, {k, n^2}] (* Michael De Vlieger, Nov 24 2016 *)

PARI

row(n)={apply(k->sqrtint(n^2\k), select(issquarefree,[1..n^2]))}
for(n=1, 6, print(row(n))) \\ Andrew Howroyd, Feb 28 2018

Formula

T(n,k) = A000196(A277646(n,A005117(k))).

T(n,k) sqrt(A005117(k)) <= n < (T(n,k)+1) sqrt(A005117(k)).

Extensions

Missing a(3009) in b-file inserted by Andrew Howroyd, Feb 28 2018