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A278101
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Triangle T(n,k) = A277648(n,k)^2 * A005117(k), read by rows.
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5
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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
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1,2
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COMMENTS
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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)).
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REFERENCES
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R. B. Eggleton, J. S. Kimberley and J. A. MacDougall, Square-free rank of integers, submitted.
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LINKS
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EXAMPLE
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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;
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MATHEMATICA
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DeleteCases[#, 0] & /@ Table[Boole[SquareFreeQ@ k] k Floor[n/Sqrt@ k]^2, {n, 7}, {k, n^2}] // Flatten (* Michael De Vlieger, Nov 24 2016 *)
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PROG
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(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)]>;
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CROSSREFS
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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STATUS
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approved
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