A278101 Triangle T(n,k) = A277648(n,k)^2 * A005117(k), read by rows.

1, 4, 2, 3, 9, 8, 3, 5, 6, 7, 16, 8, 12, 5, 6, 7, 10, 11, 13, 14, 15, 25, 18, 12, 20, 24, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 36, 32, 27, 20, 24, 28, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 49, 32, 48, 45, 24, 28, 40, 44, 13, 14, 15, 17, 19, 21, 22

Offset

1,2

Comments

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

Equivalently, the surd sqrt(T(n,k)) = A277648(n,k) * sqrt(A005117(k)).

References

R. B. Eggleton, J. S. Kimberley and J. A. MacDougall, Square-free rank of integers, submitted.

Links

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

Example

The first five rows are:
1;
4,  2,  3;
9,  8,  3,  5,  6,  7;
16,  8, 12,  5,  6,  7, 10, 11, 13, 14, 15;
25, 18, 12, 20, 24,  7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23;

Mathematica

DeleteCases[#, 0] & /@ Table[Boole[SquareFreeQ@ k] k Floor[n/Sqrt@ k]^2, {n, 7}, {k, n^2}] // Flatten (* Michael De Vlieger, Nov 24 2016 *)

Prog

(Magma)
A277647:=func<n, k|Isqrt(n^2 div k)>;
A278101_row:=func<n|[a^2*j where a is A277647(n, j):j in[1..n^2]|IsSquarefree(j)]>;
&cat[A278101_row(n):n in[1..8]];

Crossrefs

Cf. A278103.

Sequence in context: A143051 A297022 A282888 * A352416 A120240 A179394

Adjacent sequences: A278098 A278099 A278100 * A278102 A278103 A278104

Keyword

nonn,tabf,easy

Author

Jason Kimberley, Nov 15 2016

Status

approved