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A277648 Triangle T(n,k) = A277647(n, A005117(k)), read by rows.

%I A277648 #30 Mar 01 2018 03:04:49
%S A277648 1,2,1,1,3,2,1,1,1,1,4,2,2,1,1,1,1,1,1,1,1,5,3,2,2,2,1,1,1,1,1,1,1,1,
%T A277648 1,1,1,6,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,7,4,4,3,2,2,2,2,
%U A277648 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,8,5,4,3,3,3,2,2,2,2,2,1
%N A277648 Triangle T(n,k) = A277647(n, A005117(k)), read by rows.
%C A277648 The columns of this triangle are the columns of A277647 with squarefree index.
%C A277648 Other that the first (with length 1), row n has length A278100(n).
%H A277648 Jason Kimberley, <a href="/A277648/b277648.txt">Table of n, a(n) for n = 1..10716 (the first 37 rows of the triangle)</a>
%F A277648 T(n,k) = A000196(A277646(n,A005117(k))).
%F A277648 T(n,k) sqrt(A005117(k)) <= n < (T(n,k)+1) sqrt(A005117(k)).
%e A277648 Triangle begins:
%e A277648 1;
%e A277648 2, 1, 1;
%e A277648 3, 2, 1, 1, 1, 1;
%e A277648 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1;
%e A277648 ...
%e A277648 where the first 11 terms of A005117(k) are
%e A277648 1, 2, 3, 5, 6, 7,10,11,13,14,15.
%t A277648 DeleteCases[#, 0] & /@ Table[Boole[SquareFreeQ@ k] Floor[n/Sqrt@ k], {n, 8}, {k, n^2}] (* _Michael De Vlieger_, Nov 24 2016 *)
%o A277648 (Magma)
%o A277648 A277647:=func<n,k|Isqrt(n^2 div k)>;
%o A277648 A277648_row:=func<n|[A277647(n,k):k in[1..n^2]|IsSquarefree(k)]>;
%o A277648 &cat[A277648_row(n):n in[1..8]];
%o A277648 (PARI)
%o A277648 row(n)={apply(k->sqrtint(n^2\k), select(issquarefree,[1..n^2]))}
%o A277648 for(n=1, 6, print(row(n))) \\ _Andrew Howroyd_, Feb 28 2018
%Y A277648 Cf. A277646, A277647.
%K A277648 nonn,tabf,easy
%O A277648 1,2
%A A277648 _Jason Kimberley_, Nov 10 2016
%E A277648 Missing a(3009) in b-file inserted by _Andrew Howroyd_, Feb 28 2018