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A278101 Triangle T(n,k) = A277648(n,k)^2 * A005117(k), read by rows. 5
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 (list; graph; refs; listen; history; text; internal format)
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 * A120240 A179394 A102629

Adjacent sequences:  A278098 A278099 A278100 * A278102 A278103 A278104

KEYWORD

nonn,tabf,easy

AUTHOR

Jason Kimberley, Nov 15 2016

STATUS

approved

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Last modified May 9 00:09 EDT 2021. Contains 343685 sequences. (Running on oeis4.)