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%I #16 Feb 15 2017 09:31:11
%S 1,2,3,2,3,4,2,4,2,3,2,3,4,2,4,2,3,2,3,4,2,5,6,5,2,2,3,2,4,4,4,2,2,3,
%T 2,3,4,4,5,2,2,2,3,5,3,5,2,2,2,3,5,2,4,4,4,2,3,4,2,4,5,4,2,3,2,2,4,5,
%U 4,3,3,2,2,3,5,4,5,2,2,2,3,2,3,4,2,2,2,3,2,3,4,6,5,2,3,2,2,4,6,6,2,3,2
%N a(n) is the largest j such that A278101(n,k) strictly decreases for k=1..j.
%H Jason Kimberley, <a href="/A278102/b278102.txt">Table of n, a(n) for n = 1..10000</a>
%t Map[Length@ TakeWhile[FoldList[Function[s, Boole[s < 0] #2][#2 - #1] &, #], # > 0 &] &, #] &@ Map[DeleteCases[#, 0] &, Table[Boole[SquareFreeQ@ k] k Floor[n/Sqrt@ k]^2, {n, 23}, {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*k where a is A277647(n,k):k in[1..n^2]|IsSquarefree(k)]>;
%o A278102:=func<n|(exists(j){j:j in[1..#row-1]|row[j]le row[j+1]}select j else #row) where row is A278101_row(n) >;
%o [A278102(n):n in[1..103]];
%Y This is the row length sequence for triangles A278103 and A278104.
%Y A278106 lists first occurrences in this sequence.
%K nonn,easy
%O 1,2
%A _Jason Kimberley_, Nov 15 2016
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