A189151 Numbers n such that n < floor(sqrt(n)) * ceiling(sqrt(n)).

5, 10, 11, 17, 18, 19, 26, 27, 28, 29, 37, 38, 39, 40, 41, 50, 51, 52, 53, 54, 55, 65, 66, 67, 68, 69, 70, 71, 82, 83, 84, 85, 86, 87, 88, 89, 101, 102, 103, 104, 105, 106, 107, 108, 109, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 145, 146, 147, 148

Offset: 1

Author

Daniel Forgues, Apr 17 2011

Keywords

• nonn

Comments

n belongs to this sequence iff

n in (k^2,k*(k+1)), k >= 0.

See also:

n belongs to A002620 iff

n = floor(sqrt(n))*ceiling(sqrt(n)), i.e.

n = k^2 or n = k*(k+1), k >= 0.

n belongs to A063657 iff

n > floor(sqrt(n))*ceiling(sqrt(n)), i.e.

n in (k*(k+1),k^2), k >= 0.

Links

• Robert Israel, Table of n, a(n) for n = 1..10153

Crossrefs

Cf. A002620, A063657.

Programs

Maple

seq($k^2+1..k^2+k-1,k=0..20); # Robert Israel, Jan 02 2017

Mathematica

Select[Range[200], # < Floor[Sqrt[#]] Ceiling[Sqrt[#]] &] (* T. D. Noe, Apr 20 2011 *)

Python

from itertools import count, islice
def A189151_gen(): # generator of terms
    return (n for k in count(0) for n in range(k**2+1,k*(k+1)))
A189151_list = list(islice(A189151_gen(),25)) # Chai Wah Wu, Jul 28 2022

Formula

G.f.: (1-x)^(-2)-(1-x)^(-1)*(1+x+x^2-Sum_{k>=0} k*x^((k^2-5*k+8)/2)). - Robert Israel, Jan 02 2017