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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
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
KEYWORD
nonn,tabf,easy
AUTHOR
Jason Kimberley, Nov 15 2016
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)