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%I #32 Nov 18 2022 14:56:45
%S 4,9,25,36,49,64,100,121,144,169,196,225,289,324,361,400,441,484,529,
%T 576,676,729,784,841,900,961,1024,1089,1156,1225,1369,1444,1521,1600,
%U 1681,1764,1849,1936,2025,2116,2209,2304,2500,2601,2704,2809,2916,3025
%N The nonsquares squared.
%C The complement of the fourth powers A000583 within the squares A000290. - _Peter Munn_, Aug 20 2019
%H Amiram Eldar, <a href="/A030140/b030140.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A000037(n)^2.
%F Sum_{n>=1} 1/a(n) = zeta(2) - zeta(4) = A013661 - A013662 = 0.5626108331... - _Amiram Eldar_, Nov 14 2020
%F {a(n) : n >= 1} = {A225546(6m+3) : m >= 0}. - _Peter Munn_, Nov 17 2022
%e 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.
%p 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
%t a[n_] := (n + Floor[1/2 + Sqrt[n]])^2;
%t Array[a, 50] (* _Jean-François Alcover_, Apr 05 2020 *)
%o (Magma) [(n + Floor(1/2 + Sqrt(n)))^2: n in [1..60]]; // _Vincenzo Librandi_, Apr 06 2020
%Y Cf. A000037, A000290, A000583, A013661, A013662, A062503.
%Y Positions of 2's in A352080.
%Y Related to A016945 via A225546.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
%E Edited by _N. J. A. Sloane_, Jul 02 2008 at the suggestion of _R. J. Mathar_
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