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A277648 Triangle T(n,k) = A277647(n, A005117(k)), read by rows. 8
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 (list; graph; refs; listen; history; text; internal format)
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 A139100 A237982

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

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Last modified June 25 17:47 EDT 2019. Contains 324353 sequences. (Running on oeis4.)