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

1,2

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).

Links

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

Formula

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

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A277646, A277647.

Sequence in context: A145975 A211028 A239001 * A026792 A334301 A139100

Adjacent sequences: A277645 A277646 A277647 * A277649 A277650 A277651

Keyword

nonn,tabf,easy

Author

Jason Kimberley, Nov 10 2016

Extensions

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

Status

approved