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

%I A278101 #13 Nov 28 2016 00:17:43
%S A278101 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,
%T A278101 11,13,14,15,17,19,21,22,23,36,32,27,20,24,28,10,11,13,14,15,17,19,21,
%U A278101 22,23,26,29,30,31,33,34,35,49,32,48,45,24,28,40,44,13,14,15,17,19,21,22
%N A278101 Triangle T(n,k) = A277648(n,k)^2 * A005117(k), read by rows.
%C A278101 Other that the first (with length 1), row n has length A278100(n).
%C A278101 Equivalently, the surd sqrt(T(n,k)) = A277648(n,k) * sqrt(A005117(k)).
%D A278101 R. B. Eggleton, J. S. Kimberley and J. A. MacDougall, Square-free rank of integers, submitted.
%H A278101 Jason Kimberley, <a href="/A278101/b278101.txt">Table of n, a(n) for n = 1..10716 (the first 37 rows of the triangle)</a>
%e A278101 The first five rows are:
%e A278101 1;
%e A278101 4,  2,  3;
%e A278101 9,  8,  3,  5,  6,  7;
%e A278101 16,  8, 12,  5,  6,  7, 10, 11, 13, 14, 15;
%e A278101 25, 18, 12, 20, 24,  7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23;
%t A278101 DeleteCases[#, 0] & /@ Table[Boole[SquareFreeQ@ k] k Floor[n/Sqrt@ k]^2, {n, 7}, {k, n^2}] // Flatten (* _Michael De Vlieger_, Nov 24 2016 *)
%o A278101 (Magma)
%o A278101 A277647:=func<n,k|Isqrt(n^2 div k)>;
%o A278101 A278101_row:=func<n|[a^2*j where a is A277647(n,j):j in[1..n^2]|IsSquarefree(j)]>;
%o A278101 &cat[A278101_row(n):n in[1..8]];
%Y A278101 Cf. A278103.
%K A278101 nonn,tabf,easy
%O A278101 1,2
%A A278101 _Jason Kimberley_, Nov 15 2016