A213077 a(n) = round(n^2 - sqrt(n)).

0, 0, 3, 7, 14, 23, 34, 46, 61, 78, 97, 118, 141, 165, 192, 221, 252, 285, 320, 357, 396, 436, 479, 524, 571, 620, 671, 724, 779, 836, 895, 955, 1018, 1083, 1150, 1219, 1290, 1363, 1438, 1515, 1594, 1675, 1758, 1842, 1929, 2018, 2109, 2202, 2297, 2394

Offset: 0

Author

Ian Stewart, Jun 04 2012

Keywords

• nonn

Examples

			0^2 - sqrt(0) = 0;
1^2 - sqrt(1) = 0;
2^2 - sqrt(2) = 3,
3^2 - sqrt(3) = 7;
4^2 - sqrt(4) = 14.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A056847.

Programs

Maple

seq(round(n^2-sqrt(n)), n=0..100); # Robert Israel, Jul 29 2022

Mathematica

Table[Round[n^2 - Sqrt[n]], {n, 0, 100}] (* T. D. Noe, Jun 06 2012 *)

Python

count = 0
while count < 50:
    ns = count * count
    ns = ns - math.sqrt(count)
    ns = round(ns)
    print(ns, end=',')
    count += 1

Python

from math import isqrt
def A213077(n): return n**2-(m:=isqrt(n))-int((n-m*(m+1)<<2)>=1) # Chai Wah Wu, Jul 29 2022