A217570 Numbers n such that floor(sqrt(n)) = floor(n/(floor(sqrt(n))-1))-1.

9, 16, 17, 25, 26, 27, 36, 37, 38, 39, 49, 50, 51, 52, 53, 64, 65, 66, 67, 68, 69, 81, 82, 83, 84, 85, 86, 87, 100, 101, 102, 103, 104, 105, 106, 107, 121, 122, 123, 124, 125, 126, 127, 128, 129, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 169, 170, 171, 172, 173

Offset: 1

Author

Takumi Sato, Oct 07 2012

Keywords

• nonn

Comments

The sequence consists of numbers n^2+k, 0<=k<=n-3, n=3,4,5,... - M. F. Hasler, Oct 09 2012

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

Examples

			As a triangle (see the first comment) this begins:
9;
16, 17;
25, 26, 27;
36, 37, 38, 39;
49, 50, 51, 52, 53;
64, 65, 66, 67, 68, 69;
81, 82, 83, 84, 85, 86, 87;
100, 101, 102, 103, 104, 105, 106, 107; etc.
[_Bruno Berselli_, Oct 12 2012]
		

Links

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

Crossrefs

Cf. A005563, A217571, A217575.

Programs

Maple

seq($n^2 .. n^2 + n - 3, n=3..20); # Robert Israel, Dec 23 2024

PARI

is_A217570(n)={ n>3 & n\(n=sqrtint(n)-1)==n+2}  \\ - M. F. Hasler, Oct 09 2012