

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
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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, Squarefree 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, kIsqrt(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



