A030140 The nonsquares squared.

4, 9, 25, 36, 49, 64, 100, 121, 144, 169, 196, 225, 289, 324, 361, 400, 441, 484, 529, 576, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2500, 2601, 2704, 2809, 2916, 3025

Offset

1,1

Comments

The complement of the fourth powers A000583 within the squares A000290. - Peter Munn, Aug 20 2019

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000037(n)^2.

Sum_{n>=1} 1/a(n) = zeta(2) - zeta(4) = A013661 - A013662 = 0.5626108331... - Amiram Eldar, Nov 14 2020

{a(n) : n >= 1} = {A225546(6m+3) : m >= 0}. - Peter Munn, Nov 17 2022

Example

a(1)=2^2, a(2)=3^2, a(3)=5^2, a(4)=6^2, a(5)=7^2, ..., a(n)=(integer which is not a perfect square)^2.

Maple

a:=proc(n) if type(sqrt(n), integer)=false then n^2 else fi end: seq(a(n), n=1..70); # Emeric Deutsch, Apr 11 2007

Mathematica

a[n_] := (n + Floor[1/2 + Sqrt[n]])^2;
Array[a, 50] (* Jean-François Alcover, Apr 05 2020 *)

Prog

(Magma) [(n + Floor(1/2 + Sqrt(n)))^2: n in [1..60]]; // Vincenzo Librandi, Apr 06 2020
(Python)
from math import isqrt
def A030140(n): return (n+(k:=isqrt(n))+int(n>=k*(k+1)+1))**2 # Chai Wah Wu, Jun 17 2024

Crossrefs

Cf. A000037, A000290, A000583, A013661, A013662, A062503.

Positions of 2's in A352080.

Related to A016945 via A225546.

Sequence in context: A360902 A365003 A367406 * A374458 A325240 A355058

Adjacent sequences: A030137 A030138 A030139 * A030141 A030142 A030143

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Edited by N. J. A. Sloane, Jul 02 2008 at the suggestion of R. J. Mathar

Status

approved