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A217575
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Numbers n such that floor(sqrt(n)) = floor(n/floor(sqrt(n)))-1.
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5
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2, 6, 7, 12, 13, 14, 20, 21, 22, 23, 30, 31, 32, 33, 34, 42, 43, 44, 45, 46, 47, 56, 57, 58, 59, 60, 61, 62, 72, 73, 74, 75, 76, 77, 78, 79, 90, 91, 92, 93, 94, 95, 96, 97, 98, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 132, 133, 134, 135, 136
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refs;
listen;
history;
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internal format)
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OFFSET
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1,1
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COMMENTS
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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.
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
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Takumi Sato, Classification of Natural Numbers
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FORMULA
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a(n) = A063657(n) - 1. - Reinhard Zumkeller, Jun 20 2015
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EXAMPLE
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As a triangle (see the second comment) this begins:
2;
6, 7;
12, 13, 14;
20, 21, 22, 23;
30, 31, 32, 33, 34;
42, 43, 44, 45, 46, 47;
56, 57, 58, 59, 60, 61, 62;
72, 73, 74, 75, 76, 77, 78, 79;
90, 91, 92, 93, 94, 95, 96, 97, 98; etc.
- Bruno Berselli, Oct 11 2012
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MATHEMATICA
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Select[Range[200], Floor[Sqrt[#]]==Floor[#/Floor[Sqrt[#]]]-1&] (* Harvey P. Dale, Oct 06 2018 *)
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PROG
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(Visual Basic in Excel)
Sub A217575()
Dim x As Long, n As Long, y As Long, i As Long
x = InputBox("Count to")
For n = 2 To x
y = Int(Sqr(n))
If y = Int(n / y) - 1 Then
i = i + 1
Cells(i, 1) = n
End If
Next n
End Sub
(Magma) [n: n in [1..150] | Isqrt(n) eq Floor(n/Isqrt(n))-1]; // Bruno Berselli, Oct 08 2012
(PARI) is_A217575(n)=n\(n=sqrtint(n))-1==n \\ - M. F. Hasler, Oct 09 2012
(Haskell)
a217575 = subtract 1 . a063657 -- Reinhard Zumkeller, Jun 20 2015
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CROSSREFS
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Cf. A005563, A217570, A217571.
Cf. A063657.
Sequence in context: A226814 A233419 A189327 * A172154 A293531 A072147
Adjacent sequences: A217572 A217573 A217574 * A217576 A217577 A217578
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KEYWORD
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nonn
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AUTHOR
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Takumi Sato, Oct 07 2012
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STATUS
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approved
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