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%I #44 Nov 10 2012 14:27:30
%S 9,16,17,25,26,27,36,37,38,39,49,50,51,52,53,64,65,66,67,68,69,81,82,
%T 83,84,85,86,87,100,101,102,103,104,105,106,107,121,122,123,124,125,
%U 126,127,128,129,144,145,146,147,148,149,150,151,152,153,169,170,171,172,173
%N Numbers n such that floor(sqrt(n)) = floor(n/(floor(sqrt(n))-1))-1.
%C The sequence consists of numbers n^2+k, 0<=k<=n-3, n=3,4,5,... - _M. F. Hasler_, Oct 09 2012
%C One of four sequences given by classifying natural numbers according to the value of floor(sqrt(n)). See the paper in Link lines and A005563, A217571, A217575. - _Takumi Sato_, Oct 09 2012
%H Takumi Sato, <a href="http://vixra.org/abs/1210.0025">Classification of Natural Numbers</a>
%e As a triangle (see the first comment) this begins:
%e 9;
%e 16, 17;
%e 25, 26, 27;
%e 36, 37, 38, 39;
%e 49, 50, 51, 52, 53;
%e 64, 65, 66, 67, 68, 69;
%e 81, 82, 83, 84, 85, 86, 87;
%e 100, 101, 102, 103, 104, 105, 106, 107; etc.
%e [_Bruno Berselli_, Oct 12 2012]
%o (Visual Basic in Excel)
%o Sub A217570()
%o Dim x As Long, n As Long, y As Long, i As Long
%o x = InputBox("Count to")
%o For n = 2 To x
%o y = Int(Sqr(n))
%o If y = Int(n / y) Then GoTo L1
%o GoTo L2
%o L1: If y = Int(n / (y - 1)) - 1 Then
%o i = i + 1
%o Cells(i, 1) = n
%o End If
%o L2: Next n
%o End Sub
%o (PARI) is_A217570(n)={ n>3 & n\(n=sqrtint(n)-1)==n+2} \\ - _M. F. Hasler_, Oct 09 2012
%Y Cf. A005563, A217571, A217575.
%K nonn
%O 1,1
%A _Takumi Sato_, Oct 07 2012
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