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

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

Offset: 1

Author

Takumi Sato, Oct 07 2012

Keywords

• nonn

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

Examples

			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
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Takumi Sato, Classification of Natural Numbers

Crossrefs

Cf. A005563, A217570, A217571.

Cf. A063657.

Programs

Haskell

a217575 = subtract 1 . a063657  -- Reinhard Zumkeller, Jun 20 2015

Magma

[n: n in [1..150] | Isqrt(n) eq Floor(n/Isqrt(n))-1]; // Bruno Berselli, Oct 08 2012

Mathematica

Select[Range[200],Floor[Sqrt[#]]==Floor[#/Floor[Sqrt[#]]]-1&] (* Harvey P. Dale, Oct 06 2018 *)

PARI

is_A217575(n)=n\(n=sqrtint(n))-1==n  \\ - M. F. Hasler, Oct 09 2012

Formula

a(n) = A063657(n) - 1. - Reinhard Zumkeller, Jun 20 2015