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A217575 Numbers n such that floor(sqrt(n)) = floor(n/floor(sqrt(n)))-1. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
LINKS
FORMULA
a(n) = A063657(n) - 1. - Reinhard Zumkeller, Jun 20 2015
EXAMPLE
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
MATHEMATICA
Select[Range[200], Floor[Sqrt[#]]==Floor[#/Floor[Sqrt[#]]]-1&] (* Harvey P. Dale, Oct 06 2018 *)
PROG
(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
CROSSREFS
Cf. A063657.
Sequence in context: A226814 A233419 A189327 * A172154 A293531 A072147
KEYWORD
nonn
AUTHOR
Takumi Sato, Oct 07 2012
STATUS
approved

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Last modified March 19 06:05 EDT 2024. Contains 370952 sequences. (Running on oeis4.)