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A278101 Triangle T(n,k) = A277648(n,k)^2 * A005117(k), read by rows. 5

%I

%S 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 11,13,14,15,17,19,21,22,23,36,32,27,20,24,28,10,11,13,14,15,17,19,21,

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

%C Other that the first (with length 1), row n has length A278100(n).

%C Equivalently, the surd sqrt(T(n,k)) = A277648(n,k) * sqrt(A005117(k)).

%D R. B. Eggleton, J. S. Kimberley and J. A. MacDougall, Square-free rank of integers, submitted.

%H 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 The first five rows are:

%e 1;

%e 4, 2, 3;

%e 9, 8, 3, 5, 6, 7;

%e 16, 8, 12, 5, 6, 7, 10, 11, 13, 14, 15;

%e 25, 18, 12, 20, 24, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23;

%t 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 (Magma)

%o A277647:=func<n,k|Isqrt(n^2 div k)>;

%o A278101_row:=func<n|[a^2*j where a is A277647(n,j):j in[1..n^2]|IsSquarefree(j)]>;

%o &cat[A278101_row(n):n in[1..8]];

%Y Cf. A278103.

%K nonn,tabf,easy

%O 1,2

%A _Jason Kimberley_, Nov 15 2016

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Last modified June 13 03:36 EDT 2021. Contains 344980 sequences. (Running on oeis4.)