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A217575 Numbers n such that floor(sqrt(n)) = floor(n/floor(sqrt(n)))-1.

%I A217575 #38 Sep 08 2022 08:46:04
%S A217575 2,6,7,12,13,14,20,21,22,23,30,31,32,33,34,42,43,44,45,46,47,56,57,58,
%T A217575 59,60,61,62,72,73,74,75,76,77,78,79,90,91,92,93,94,95,96,97,98,110,
%U A217575 111,112,113,114,115,116,117,118,119,132,133,134,135,136
%N A217575 Numbers n such that floor(sqrt(n)) = floor(n/floor(sqrt(n)))-1.
%C A217575 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, A217570, A217571.
%C A217575 Can be interpreted as a triangle read by rows: T(n,k) = n*(n+1)+k-1 with n>0, k=1..n. - _Bruno Berselli_, Oct 11 2012
%H A217575 Reinhard Zumkeller, <a href="/A217575/b217575.txt">Table of n, a(n) for n = 1..10000</a>
%H A217575 Takumi Sato, <a href="http://vixra.org/abs/1210.0025">Classification of Natural Numbers</a>
%F A217575 a(n) = A063657(n) - 1. - _Reinhard Zumkeller_, Jun 20 2015
%e A217575 As a triangle (see the second comment) this begins:
%e A217575 2;
%e A217575 6, 7;
%e A217575 12, 13, 14;
%e A217575 20, 21, 22, 23;
%e A217575 30, 31, 32, 33, 34;
%e A217575 42, 43, 44, 45, 46, 47;
%e A217575 56, 57, 58, 59, 60, 61, 62;
%e A217575 72, 73, 74, 75, 76, 77, 78, 79;
%e A217575 90, 91, 92, 93, 94, 95, 96, 97, 98; etc.
%e A217575 - _Bruno Berselli_, Oct 11 2012
%t A217575 Select[Range[200],Floor[Sqrt[#]]==Floor[#/Floor[Sqrt[#]]]-1&] (* _Harvey P. Dale_, Oct 06 2018 *)
%o A217575 (Visual Basic in Excel)
%o A217575 Sub A217575()
%o A217575 Dim x As Long, n As Long, y As Long, i As Long
%o A217575 x = InputBox("Count to")
%o A217575 For n = 2 To x
%o A217575 y = Int(Sqr(n))
%o A217575 If y = Int(n / y) - 1 Then
%o A217575 i = i + 1
%o A217575 Cells(i, 1) = n
%o A217575 End If
%o A217575 Next n
%o A217575 End Sub
%o A217575 (Magma) [n: n in [1..150] | Isqrt(n) eq Floor(n/Isqrt(n))-1]; // _Bruno Berselli_, Oct 08 2012
%o A217575 (PARI) is_A217575(n)=n\(n=sqrtint(n))-1==n  \\ - _M. F. Hasler_, Oct 09 2012
%o A217575 (Haskell)
%o A217575 a217575 = subtract 1 . a063657  -- _Reinhard Zumkeller_, Jun 20 2015
%Y A217575 Cf. A005563, A217570, A217571.
%Y A217575 Cf. A063657.
%K A217575 nonn
%O A217575 1,1
%A A217575 _Takumi Sato_, Oct 07 2012